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Tutors Answer Your Questions about Conjunction (FREE)
Question 268417: I dont understand questions like this.
p:An isosceles triangle has two congruent sides.
q:A right angle measures 90 degrees
r:Four points are always coplanar
s:A decagon has 12 sides
Answer by mspretty(2)   (Show Source):
Question 267283: If p is a true statement and q is a false statement then find the truth value of q^(p^q)
Answer by jim_thompson5910(14863) (Show Source):
You can put this solution on YOUR website!Hint: recall that p ^ q is only true if BOTH p AND q are true. Otherwise, p ^ q is false. To get you started, since p is true, but q is false, we know that p ^ q is false (since q is false). I'll let you continue.
Question 263743: Given p is true, q is false, and r is true, find the truth value of the statement (~p ^ q) ↔ ~r.
its true.
i made a truth table but i think im wrong
Answer by jim_thompson5910(14863) (Show Source):
You can put this solution on YOUR website!If p is true, then ~p is false (since ~p is the opposite of p).
Remember that "^" means "and". The statement p ^ q is only true if BOTH p AND q are true (hence the "and"). Since ~p is false, we automatically know that ~p ^ q is false (q doesn't have to be factored in at all).
Finally, remember that p <-> q is only true if the truth values for p and q are the same. So if p and q are both true, or both false, then p <-> q is true. Think of this as an "equals" (ie p = q). Because r is true, ~r is false. Since ~p ^ q is false as well, ~p ^ q and ~r have the same truth values. So (~p ^ q) <-> ~r is true. So you are correct. Good job.
Here's one way you could write all this out:
(~p ^ q) <-> ~r
(~T ^ F) <-> ~T
(F ^ F) <-> F
F <-> F
T
Question 263311:
Hello Sir
Sir, does this mean there is some sort of relativity between the god of lies' reply and god of truths' reply ?
The question is
You are stranded on an Island and on that island are 3 all knowing all powerful gods. One god is the god of truth, who always tells the truth and can never lie. The second god is the god of lies, he always lies and never tells the truth. The 3rd god is the god of chaos, he tells both lies and truths, however, completely randomly. The gods appear as identical twins, they all look the same. The gods also speak a language that you do not understand, except that you know that A and B are the responses yes and no (you however do not know which word is yes and which is no). You can only ask 3 yes or no questions to the gods in order to figure out which god is which. What 3 questions do you ask?
I answered :
Number the gods 1, 2, and 3.
“if I ask 3rd god of chaos 'you are one god of truth, who always tells the truth, right?' what would 3rd God
say?"
Then, one god : can't reply. <- that's because one god is the god of truth,who always tells the truth but he don't know what 3rd god would say.
2nd god : Yes or No.
3rd god : Yes or No.
*Surely, both 3rd and 2nd God will reply, yes or no whatever.
EXAMPLE-
# 1.
Ask god 1 and 2 : “if I ask 3rd god of chaos 'you are one god of truth, who always tells the truth, right?' what would 3rd God
say?"
God 1 : reply = Yes or No
God 2 : reply = Yes or No
#2.
Ask god 3 : "f I ask 3rd god of chaos 'you are one god of truth, who always tells the truth, right?' what would 3rd God
say?"
God 3 : = Can't reply.
#3.
Ask God 3 : " is god 2 god of lies,who always lies ? "
God 3 : = Yes.
hence, god 1 = god of chaos
god 2 = god of lies
god 3 = god of truths
or
Answer 2 :
Number the gods 1, 2, and 3. Ask god 1: Would god 2 say that 2+2=4? If he answers, then remember his answer and ask god 2: would god 3 say that 2+2=4?
If god 1 doesn't answer your question then god 2 is the chaos god. You now have 2 questions to determine which god is which from gods 1 and 2. So ask god 1: would god 3 say that 2+2=4?
If god 2 doesn't answer your question then god 3 is the chaos god. You have god 1's answer. And if gods 1 and 2 both answer, then god 1 is the chaos god and you have god 2's answer.
So you've pinpointed the chaos god. Call the remaining gods A and B, so that A is the one who you have already asked the "would god B say that 2+2=4" question of.
However god A answered, it meant "no," so now you know which word is "no." Now ask god A, "would god B say you are the lying god?" If he says yes, god A is the truth telling god and god B is the liar; if he says no, god A is the liar and god B is the truth telling god.
Thank you.
Sincerely,
Brooke ga-eul Kim
Answer by richwmiller(3479) (Show Source):
You can put this solution on YOUR website!Why do you think that one of them can't or doesn't reply?
One always tells the truth.
One always lies,
and one randomly answers sometimes answers the truth and sometimes lies.
BTW Why do you address the question to "sir"? There are female tutors! and many men don't like being called sir.
http://www.rule0.com/archives/148
and
http://www.physicsforums.com/archive/index.php/t-36932.html
Question 263274: 7. Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement.
[(~q V r) Λ~p]
(Points :3)
True
False
i picked true
Answer by mducky2(62) (Show Source):
You can put this solution on YOUR website!Let's put this into words and simplify it. We know that V = or, ~ = not, and Λ = and.
[(~q V r) Λ~p]
[((not q) or r) and not p]
Now let's plug in true (T) or false (F) for all the letters. According to the problem, p = T, q = F, and r = F.
[((not q) or r) and not p]
[((not F) or F) and not T]
We can simplify this down by replacing "not F" with "T" and "not T" with "F".
[((not F) or F) and not T]
[(T or F) and F]
For "or" equations, the equation is true if either one is true. Since one is true, it becomes T.
[(T or F) and F]
[T and F]
For "and" equations, the equation is true only if both are true. Since one is not true, it becomes F.
[F]
The answer is false.
Question 263168: Hello,
Can someone please help me with a truth table, I am the worst in trying to fiqure them out but I tried here what I did
Fill in the heading of the following truth table using any of p, q, ~, , ↔, , and . Use keyboard shortcuts of --> for , <--> for ↔, V for , and ^ for .
p.......q........P<->q
T.......T........T
T.......F........T
F.......T........F
F.......F........T
I not sure I did that right, I'm so confused with these type of problem and I have more to do.
Thank you so much for your help, I'm new to this web site a friend recommended you site to me.
Again Thank you I hope you can help me.
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(14863) (Show Source):
You can put this solution on YOUR website!Recall that the truth table for p -> q is
p.......q........p -> q
T.......T........T
T.......F........F
F.......T........T
F.......F........T
In other words, p -> q is only false when p is true and q is false. This is like saying that "if it rains, then it will be wet outside". If it does rain, but doesn't get wet, then the statement is false. In any other case, p -> q is true.
If we swap p and q to get q -> p, we then get
p.......q........q -> p
T.......T........T
T.......F........T
F.......T........F
F.......F........T
So the proper heading for the last column is q -> p
Answer by stanbon(29482) (Show Source):
You can put this solution on YOUR website!It is almost impossible to display
the proper ordering of a truth
table on this site. May I suggest
you Google "truth table examples".
There you will see worked examples
that may help you.
Check the Wikipedia site on truth tables.
Cheers,
Stan H.
Question 262909: Determine the truth value of the following statement:
Rome is a city in France or all numbers are divisible by 1.
Answer by richwmiller(3479) (Show Source):
Question 262318: Hello,
Can someone please help me solve this problem, I tried and I still can not figure it out. I really stuck on this problem.
a) Construct a truth table for (~p UD ^ q) ↔ q
Thank you,
Answer by richwmiller(3479) (Show Source):
Question 262147: 8. Determine which, if any, of the three statements are equivalent. Give a reason for your conclusion. Show complete work.
I) If the dog licks her nose, then the dog is not happy.
II) If the dog licks her nose, then the dog is happy.
III) If the dog is not happy, then the dog does not lick her nose.
a. I, II, and III are equivalent
b. I and II are equivalent
c. II and III are equivalent
d. I and III are equivalent
e. None are equivalent
How do I show work on this? I don't get it?
Found 2 solutions by richwmiller, jim_thompson5910:
Answer by richwmiller(3479) (Show Source):
You can put this solution on YOUR website!I and II are contradictory and so not true.
II and III are called contrapositives and are therefore true by definition and for the same reason I and III are not true.
Answer by jim_thompson5910(14863) (Show Source):
You can put this solution on YOUR website!Here's the basic outline to solving this problem
Step 1) Assign p: the dog licks her nose and q: the dog is happy
Step 2) Translate each statement into symbolic form.
Step 3) Create a table for each symbolic statement. Any tables which have equivalent final columns will be equivalent expressions.
For example, translate "If the dog licks her nose, then the dog is not happy. " into p -> ~q and set up the following table
| p | q | ~q | p -> ~q |
| T | T | F | F | | T | F | T | T | | F | T | F | T | | F | F | F | T |
Do the same for the 2 other statements and compare the last columns in the table. Let me know if this helps.
Question 261925: Write the compound statement is words.
Let p= The monitor is included.
Let q= The color printer is optional
a) The monitor is not included and the color printer is optional.
b) The monitor is included and the color printer is not optional.
c) The monitor is included and the color printer is optional.
d) The monitor is inlcuded or the color printer is not optional.
I think the answer is "d", am I correct?
Answer by dylantc77(2) (Show Source):
Question 261914: Can someone tell me if I have this correct?
Identify which argument is invalid?
1) If I catch the bus on time, then I am not late to work.
I was late to work
Therefore, I did not catch the bus on time.
2) If I shower in the morning, then I do not smell bad.
I do not smell bad.
Therefore, I showered in the morning.
3) Either I catch the bus on time or I am late to work.
I did not catch the bus on time.
Therefore, I was late to work.
4) If the water is filtered, then it will not contain lead.
The water is filtered.
Therefore, it does not contain lead.
5) If the elephant roars, then it does not want company.
If it does not want company, then it is hungry.
If the elephant roars, then it is hungry.
I think the answer is number 5, am I correct?
Answer by alyssab92(4) (Show Source):
Question 261773: In this exercise, construct a truth table for the statement
~p --> ~q
Answer by jim_thompson5910(14863) (Show Source):
You can put this solution on YOUR website!Hint: Recall that p -> q is only false when p is true and q is false. Here's the truth table for p -> q.
Use this idea to find the table for ~p -> ~q
Question 261189: Can someone please help me with these truth tables? When I get my tax check I am planning on making a donation to the site because this site has really helped me out alot. This is 3 tables out of a slew I have and I really need help on these, so I can do the rest of my work.
1) (q ^ ~q) <-> q
2)(~p ^ q) -> p
3) q -> (q V ~q)
Thank you soooo much in advance for your time and effort to help me...
Answer by jim_thompson5910(14863) (Show Source):
You can put this solution on YOUR website!# 1
Is there supposed to be a 'p' somewhere in there? Please double check it.
# 2
I'll do the second one to get you going. If this isn't enough, either ask me or repost.
Start with a blank table with 4 rows and with the headers of p, q, ~p, ~p ^ q, (~p ^ q) -> p. The headers are simply smaller pieces of (~p ^ q) -> p
Fill in T, T, F, F in the first column and T, F, T, F in the second. This will exhaust all of the possible truth combinations of p and q
| p | q | ~p | ~p ^ q | (~p ^ q) -> p | | T | T | | | | | T | F | | | | | F | T | | | | | F | F | | | |
Negate the first column p to get ~p for the third column
| p | q | ~p | ~p ^ q | (~p ^ q) -> p | | T | T | F | | | | T | F | F | | | | F | T | T | | | | F | F | T | | |
Recall that p ^ q is only true when BOTH p and q are true. Otherwise it is false. So ~p ^ q is only true when the corresponding entries of the columns ~p and q are both T, or otherwise it's false. Use this info to fill in the fourth column.
| p | q | ~p | ~p ^ q | (~p ^ q) -> p | | T | T | F | F | | | T | F | F | F | | | F | T | T | T | | | F | F | T | F | |
Now remember that p -> q is only false when p is true, but q is false (otherwise, it is true). This is like me claiming "if it rains, then it gets wet". If it does rain, but it does not get wet, then my statement is false. Fortunately for us, much of the fourth column is false which will make much of the last column true. Let's now use this information to complete the table.
| p | q | ~p | ~p ^ q | (~p ^ q) -> p | | T | T | F | F | T | | T | F | F | F | T | | F | T | T | T | F | | F | F | T | F | T |
Question 261272: Write the argument belowin symbols to determine whether it is valid or invalid. State a reason for your conclusion. Specify the p and q you used.
If the koi are swimming in the pond, then the birds are chirping.
The koi are not swimming in the pond.
The birds are not chirping.
I am so confused and need help please.
Answer by solver91311(6089)  (Show Source):
Question 261207: Form the contrpositive: If I do not wash my clothes, then I will have nothing clean to wear.
a) If I have nothing clean to wear, I did not wash my clothes.
b) If I do not wash my clothes, then I will have something clean to wear
c) If i wash my clothes, then I will have something clean to wear.
d) If I have something clean to wear, I washed my clothes.
e) If I have something clean to wear, I did not wash my clothes.
I know b and e doesn't make sense, but the rest all look the same to me.
Answer by solver91311(6089) (Show Source):
You can put this solution on YOUR website!
Just follow the pattern for creating a contrapositive:
Take the opposite of the conclusion and make that the new premise. The original conclusion is "I will have nothing clean to wear" The opposite of that is "I have something clean to wear" and now the premise of the contrapositive is:
If I have something clean to wear.
Take the opposite of the original premise and make that the new conclusion. The original premise: "If I do not wash my clothes..." The opposite: "I washed my clothes."
So the entire contrapositive becomes:
If I have something clean to wear, then I washed my clothes.
Choice d.
John
Question 261276: Fill in the heading of the following truth table using any of p, q, ~, ->, <->, V, and ^.
q q fill in here
T T F
T F T
F T T
F F F
Answer by jim_thompson5910(14863) (Show Source):
Question 261274: Given p is true, q is true, and r is false, find the truth value of the statement: ~ p (q v ~r).
Please show step by step work, so I can do my other problems.
Found 2 solutions by solver91311, drk:
Answer by solver91311(6089) (Show Source):
Answer by drk(1905) (Show Source):
You can put this solution on YOUR website!p . . . . .q . . . . . r . . . . . ~r . . . . . .~p . . . . . (q v ~r) . . . . . . .~ p n (q v ~r) . . . . . . . ~ p v (q v ~r)
T . . . . . T. . . . .T. . . . . . F. . . . . . . F. . . . . . .T . . . . . . . . . . . . . . . .T. . . . . . . . . . . . . . . .T
T. . . . . F. . . . . T. . . . . . F. . . . . . . F. . . . . . .F . . . . . . . . . . . . . . . .F. . . . . . . . . . . . . . . .T
T. . . . . T. . . . . F. . . . . . T. . . . . . . F. . . . . . .T . . . . . . . . . . . . . . . .T. . . . . . . . . . . . . . . .T
T. . . . . F. . . . . F.. . . . . . T. . . . . . .F. . . . . . .T . . . . . . . . . . . . . . . .T. . . . . . . . . . . . . . . .T
F. . . . . T. . . . . T. . . . . . F. . . . . . .T. . . . . . .T . . . . . . . . . . . . . . . .F. . . . . . . . . . . . . . . .T
F. . . . . F. . . . . T. . . . . . F. . . . . . .T. . . . . . .F . . . . . . . . . . . . . . . .F. . . . . . . . . . . . . . . .F
F. . . . . T. . . . . F. . . . . . T. . . . . . .T. . . . . . .T . . . . . . . . . . . . . . . .F. . . . . . . . . . . . . . . .T
F. . . . . F. . . . . F. . . . . . T. . . . . . .T. . . . . . .T . . . . . . . . . . . . . . . .F. . . . . . . . . . . . . . . .T
---
since I didn't see an operation between ~p and (q v ~r) I did both.
Question 261282: I made a mistake in posting my original problem sorry..here is the correct one
Given p is true, q is true, and r is false. find the truth value of the statement: ~p -> (q v ~ r)
Show step by step work so I can use as example for other problems...
Thanks in advance soooo much..
Answer by jim_thompson5910(14863) (Show Source):
You can put this solution on YOUR website!Some things to remember:
1) ~p is the opposite of p. So if p is true, then ~p is false (or vice versa).
2) p v q is true when either p or q is true (or both are true)
3) p -> q is only false when p is true, but q is false. Otherwise, it is true.
~p -> (q v ~ r) ... Start with the given compound statement
~T -> (T v ~ F) ... Plug in T for p (true), T for q (true), and F for r (false)
F -> (T v T) ... Evaluate ~T to get F. Evaluate ~F to get T
F -> T ... Evaluate T v T to get T
T ... Evaluate F -> T to get T
So ~p -> (q v ~ r) is true when p is true, q is true, and r is false
Question 261208: Write the compound statement in symbols.
Let r= The food is good, p= I eat too much, q= I'll exercise
If the food is good or if I eat too much, I'll exercise.
a) r -> (p V q)
b) (r V p) -> q
c) (r -> p) ->q
d) (r ^ p) -> q
I can't seem to get the idea of using the symbols, I have tried and tried, please help me.
Answer by jim_thompson5910(14863) (Show Source):
You can put this solution on YOUR website!Remember that V stands for 'or'. So "p V q" stands for "p or q"
This means that "the food is good or if I eat too much" turns into "r V p".
Also, p -> q means "if p, then q". So "If the food is good or if I eat too much, I'll exercise" then becomes "(r V p) -> q"
So the final answer is (r V p) -> q
Question 261270: Determine the truth value of the following statement:
Leonhard Euler was a famous mathematician and the sum of any two odd numbers is an even number.
Is this true or false?
Answer by solver91311(6089) (Show Source):
You can put this solution on YOUR website!
In order for a statement consisting of two statements joined by "and" to be a true statement, both of the constituent statements must be true. Let us first examine the second of your two constituent statements. The  -th odd number is  . The  -th odd number is  . The sum of these two odd numbers is then:
\ +\ \left(2m\,-\,1\right)\ =\ 2n\,+\,2m\,-\,2)
The sum is clearly divisible by 2 and is therefore an even number, hence the second part of the compound statement is true.
So, it all comes down to your definition of "famous mathematician." If you believe that Herr Euler was a mathematician and that he was famous, whatever that means, then the first part of the compound statement is true. It is very possible that the statement posed is true for some people and false for others. For example, I would unhesitatingly say that the statement is true, because I believe Leonhard Euler to be not only "a" famous mathematician, but "the" famous mathematician. Other people, deplorably ignorant in my view, have never heard of him and therefore must deny the statement.
John
Question 261271: Determine which, if any, of the three statements are equivalent.
I) If the weather is not warm, then I will need a sweater.
II) Either I will not need a sweater or the weather is not warm.
III) If I will not need a sweater, then the weather is warm.
a) I and II are equivalent
b) I and III are equivalent
c) II and III are equivalent
d) I, II, and III are equivalent
e) None are equivalent
Answer by richwmiller(3479) (Show Source):
Question 261150: Determine which, if any, of the three statements are equivalent.
I) If I am hungry, then I will not be able to concentrate at the meeting.
II) Either I am not hungry or I will be able to concentrate at the meeting.
III) If I am able to concentrate at the meeting, then I am not hungry.
Choices:
a) I,II, and III are equivalent
b) I and II are equivalent
c) I and III are equivalent
d) None are equivalent
I am lost here, I really need some help please.
Answer by richwmiller(3479) (Show Source):
Question 260703: Let p represent the statement, "Jim plays football", and let q represent "Michael plays basketball". Convert the compound statements into symbols.
It is not the case that Jim does not play football or Michael plays basketball.
I am not getting this symbol stuff at all..Please help me.
Answer by jim_thompson5910(14863) (Show Source):
You can put this solution on YOUR website!Let
p: Jim plays football
q: Michael plays basketball
So what this means is that wherever you see a 'p', it will essentially stand for "Jim plays football". Think of this as talking in code.
The symbol ~ stands for the negation of a given statement. So ~p means NOT p. It is the opposite of what p represents. So if p: Jim plays football, then ~p: Jim does NOT play football. You can see that p and ~p are opposites of each other.
Also, the symbol  stands for "or"
First, take a look at the statement "Jim does not play football or Michael plays basketball". We;re going to ignore the beginning part "It is not the case" for now.
So "Jim does not play football" translates to  and "Michael plays basketball" translates to  . Combine the two symbols with a to get  (since we're dealing with an 'or' situation)
Finally, negate the entire statement by placing a  outside the parenthesis to get ) . We're doing this because the beginning of the sentence states that "it is not the case" which means that we take the opposite of whatever the remaining sentence is claiming.
So the full translation of "It is not the case that Jim does not play football or Michael plays basketball" is
Question 260705: Write the statement in symbols using the p and q given below. Then construct a truth table for the symbolic statement.
p=I eat too much
q=I'll exercise
I'll excercise if I don't eat too much.
Answer by drk(1905) (Show Source):
You can put this solution on YOUR website!here is the statement:
I'll excercise if I don't eat too much.
turn this around so that we start with if, we get
"if I don't each too much, then I'll exercise"
This is represented symbolically as
~p -> q
truth table:
p . . . . . . .~p . . . . . . .q . . . . . . . ~p-> q
T . . . . . . .F . . . . . . . . T . . . . . . . .T
T . . . . . . F . . . . . . . . .F . . . . . . . . .T
F . . . . . . .T . . . . . . . .T . . . . . . . . .T
F. . . . . . . T . . . . . . . F . . . . . . . . .F
Question 260706: Determine if the argument is valid or invalid. Give a reason to justity answer.
If you eat well, you will be well.
If you are well, you will be happy.
If you eat well, you will be happy.
choices are as follow:
a) Valid by the law of detachment
b) Valid by the law of contraposition
c) Invalid by fallacy of the converse
d) Invalid by fallacy of the inverse
e) Valid by the law of syllogism
f) Valid by disjunctive syllogism
Answer by drk(1905) (Show Source):
You can put this solution on YOUR website!If you eat well, you will be well.
p -> q
If you are well, you will be happy.
q -> r
If you eat well, you will be happy.
p -> r
---
answer is
e) Valid by the law of syllogism
Question 260704: Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement.
(p V ~q) or r, I had to type the word "or" since I don't know how to type in the upside down V.
Is this statement true or false?
Please show me how you got the answer so I can learn from it.
Answer by drk(1905) (Show Source):
You can put this solution on YOUR website!p = true
q = false - - -> ~q = true
r = false
--
(p V ~q) - -> (T or T) = T
(p V ~q) V r - - - > (T or T) or F - - > T or F - - > T
Question 260500: I have to construct a truth table for 2 different problems I am having a horrible time understanding how to do this.
Problem 1: ~q V p
Problem 2: (p ^ ~q) "if and only then" q The mark in the middle of p and ~q is suppose to be upside V, for "and".
Please show me how to do these 2 problems, I have trying for a couple of hours and I am completely lost.
Answer by drk(1905) (Show Source):
You can put this solution on YOUR website!Problem 1: ~q V p - -> I translate this as not q union "or" p
here is the truth table for this:
p . . . . .q . . . . .~q . . . . . ~q V p
T . . . . .T . . . . .F . . . . . . . . . T
T . . . . .F . . . . .T . . . . . . . . .T
F . . . . .T . . . . . F . . . . . . . . .F
F . . . . .F . . . . .T . . . . . . . . . T
Problem 2: (p ^ ~q) - - > I translate this as p intersection "and" not q
here is the truth table for this:
p . . . . .q . . . . .~q . . . . . p ^ ~q
T . . . . .T . . . . .F . . . . . . . . . F
T . . . . .F . . . . .T . . . . . . . . .T
F . . . . .T . . . . . F . . . . . . . . .F
F . . . . .F . . . . .T . . . . . . . . . F
Question 259684: If the average of s and t is 25, and t is equal to the average of w and x, what is the value of 2s in terms of w and x?
(A) 25 + w + x (B) 25 - w - x (C) 50 - w - x (D) 50- 2w - 2x (E) 100 - 2w - 2x
Found 3 solutions by studant, Fombitz, stanbon:
Answer by studant(1) (Show Source):
Answer by Fombitz(2595)  (Show Source):
You can put this solution on YOUR website!
1. 
.
.
2. 
From eq. 1,
Then using eq. 2,
None of the above.
.
.
.
As a supporting example,
let  ,  , 
let  ,  , 
then 
so that equation is correct.
The answer should be
Answer by stanbon(29482) (Show Source):
You can put this solution on YOUR website!If the average of s and t is 25, and t is equal to the average of w and x, what is the value of 2s in terms of w and x?
---------------------------------
(s + t)/2 = 25
So, s+t = 50
----------------------------
t = (w+x)/2
---
Substitute for "t" and solve for "s":
s + (w+x)/2 = 50
2s + w + x = 100
2s = [100 -w -x]
------------------------
Cheers,
Stan H.
(A) 25 + w + x (B) 25 - w - x (C) 50 - w - x (D) 50- 2w - 2x (E) 100 - 2w - 2x
Question 253525: My brain is 54 years old and it is trying to understand discrete structures. My first hurdle is creating a truth table for ~(p^q) v (pvq). Maybe I should withdraw from my class??? :-) I appreciate any assistance.
Found 2 solutions by Edwin McCravy, solver91311:
Answer by Edwin McCravy(3594) (Show Source):
You can put this solution on YOUR website!
~(p^q) v (pvq).
Letters stand for sentences. Some sentences are true and some are false.
Fro example let p = "Today is Monday" and q = "This month is August".
Sometimes p is true and q is true, say on a Monday in August.
Sometimes p is true and q is false, say on a Monday in March.
Sometimes p is false and q is true, say on a Tuesday in August.
Sometimes p is false and q is false, say on a Tuesday in March.
~(p^q) v (pvq).
That says:
It's not both Monday and August or it's Monday or August.
That's a compound sentence and it is hard to analyze, just reading it.
That's why we need truth tables to sort out the various possibilities
There are only four possibilities to consider.
1. p is true and q is true
2. q is true and q is false
3. p is false and q is true
4 p is false and q is false
So we start with those four possibilities in a table:
The binary operators are ^ and v, "and" and "or". They always have letters
on both sides of them.
The unary operator is ~, "not". It can only have one letter on the right
side of it.
^ means "and". In order to be true it must have true statements on both
sides of it. It is false any other time.
v means "or". In order for it to be true it only needs to have just one
true statement on either side of it. It is only false when it has false
sentences on BOTH sides.
~ before a letter means that the sentence that follows it is false.
So the truth table for a statement that has two sentences, that is,
letters, p and q, starts out as this:
p q
case 1 T T
case 2 T F
case 3 F T
case 4 F F
To build a truth table for ~(p^q) v (pvq)
we have to make headings for each of these:
A. p
B. q
C. (p^q)
D. ~(p^q)
E. (pvq)
F. ~(p^q) v (pvq)
We start with the four cases for letters p, q, steps A and B
we can build C from A and B
We can build D from C
We can build E from A and B
We can build F from D and E
So we start with this:
p q | (p^q) | ~(p^q) | (pvq) | ~(p^q) v (pvq) |
case 1 T T | | | | |
case 2 T F | | | | |
case 3 F T | | | | |
case 4 F F | | | | |
We fill the (p^q) column using the rule for "and".
Case 1 has a T under p and a T under q.
That's both T's, so the (p^q) column gets a T, for case 1.
Case 2 has a T under p and a F under q,
That's not both T's, so the (p^q) column gets a F for case 2.
"And" needs 2 T's to be true.
Case 3 has a F under p and a T under q,
That's not both T's, so the (p^q) column gets a F for case 3.
"And" needs 2 T's to be true.
Case 4 has a F under p and a F under q,
That's certainly not both T's, so the (p^q) column gets a F for case 4.
"And" needs 2 T's to be true.
So the cases under (p^q) go "TFFF"
p q | (p^q) | ~(p^q) | (pvq) | ~(p^q) v (pvq) |
case 1 T T | T | | | |
case 2 T F | F | | | |
case 3 F T | F | | | |
case 4 F F | F | | | |
Now to fill in the next column, we notice it has "~" or "not" before
(p^q), so we put the exact opposite of what is in the (p^q) column. The
(p^q) column has "TFFF", so the ~(p^q) column has "FTTT":
p q | (p^q) | ~(p^q) | (pvq) | ~(p^q) v (pvq) |
case 1 T T | T | F | | |
case 2 T F | F | T | | |
case 3 F T | F | T | | |
case 4 F F | F | T | | |
Next we fill in the (pvq) column.
Case 1 has a T under p and a T under q.
All "v" needs is at least 1 T on either or both sides of it. p has a T
and Q has a T, so that's at least one T on at least one side of "v", so
case 1 gets a T.
Case 2 has a T under p and an F under q.
All "v" needs is at least 1 T on either or both sides of it. p has a T
and Q has a F, so that's at least one T on at least one side of "v", so
case 2 gets a T.
Case 3 has a F under p and a T under q.
All "v" needs is at least 1 T on either or both sides of it. p has a F
and Q has a T, so that's at least one T on at least one side of "v", so
case 3 gets a T.
Case 4 has a F under p and a F under q.
But "v" needs at least 1 T on either or both sides of it to be true. It does
NOT have T on either side of it in case 4, so case 4 gets an F.
So the (pvq) column goes TTTF
p q | (p^q) | ~(p^q) | (pvq) | ~(p^q) v (pvq) |
case 1 T T | T | F | T | |
case 2 T F | F | T | T | |
case 3 F T | F | T | T | |
case 4 F F | F | T | F | |
Now we just have one more column to fill in. It has "v" or "OR" between
what's in the previous two columns, ~(p^q), (pvq). All we need in order to
put a true in that column is for just at least ONE of the preceding two
columns to have a T in it.
Case 1 has a F under ~(p^q) and a T under (pvq),
That's at least one T, so the last column gets a T, for case 2.
Case 2 has a T under ~(p^q) and a T under (pvq),
That's at least one T, so the last column gets a T for case 2.
Case 3 has a T under ~(p^q) and a T under (pvq),
That's at least one T, so the last column gets a T for case 3.
Case 4 has a T under ~(p^q) and an F under (pvq),
That's at least one T, so the last column gets a T for case 4.
So the final column gets filled in TTTT.
That means the statement is ALWAYS true in EVERY case. Since that happened
we say ~(p^q) v (pvq) is ALWAYS true regardless of whether p or q is true or
false. That's called a "tautology".
By the way, the fancy word for "and" ("^") is "conjunction.
The fancy word for "or" ("v") is "disjunction".
The fancy word for "not" ("~") is "negation".
Edwin
Answer by solver91311(6089) (Show Source):
You can put this solution on YOUR website!
I can show you this with an explanation, but rendering it here is a real pain in the rear end. Write back and I'll reply with the solution on an attached document.
John
Question 248506: Determine whether the argument is valid or invalid.
All B is C.
All C is A.
All B is A.
Answer by stanbon(29482) (Show Source):
You can put this solution on YOUR website!Determine whether the argument is valid or invalid.
All B is C.
All C is A.
All B is A.
---------------------
Valid by the transitive law.
Cheers,
Stan H.
Question 203549: please help
) Determine which, if any, of the three statements are equivalent.
a) If today is Monday, then tomorrow is Tuesday.
b) If today is not Monday, then tomorrow is not Tuesday.
c) If tomorrow is not Tuesday, then today is not Monday
Answer by College Student(480)  (Show Source):
You can put this solution on YOUR website!Statements B and C are equivalent because they state the same thing, only in different order.
.
Statement A, while it makes sense, it is limited to Monday and Tuesday.
Question 232782: please help me slove this question .
Construct a truth table for each compound statement.
1-q ∨ (p ∧ ∼q)
2- ∼q ∧ (∼ p ∨ ∼q)
Answer by vleith(2079) (Show Source):
You can put this solution on YOUR website!Let's do the first one, then you cna use the same technique to do the second one
Create a table that has 5 rows (one for the headings, one each for the combination of 0 and 1 for the variables p and q)
Then add an column for each 'term' in the given logical statement. In this case, you need p, q, ~q, (p^~q) and finally p v (p^~q). So you need 5 columns, as shown below.
Then add in the true/false (1/0) entries for p and q. Since there are two variables with two possible values, you have 2*2 total. Or 4 rows of info.
p q ~q (p^~q) pv(p^~q)
0 0
1 0
1 0
1 1
Now complete the ~q column, given the entered values for p and q
p q ~q (p^~q) pv(p^~q)
0 0 1
1 0 1
0 1 0
1 1 0
Now complete the (p^~q) column, given the entered values for p and ~q
p q ~q (p^~q) pv(p^~q)
0 0 1 1
1 0 1 1
0 1 0 0
1 1 0 1
Finally complete the pv(p^~q) column, given the entered values for p and (p^~q)
p q ~q (p^~q) pv(p^~q)
0 0 1 0 0
1 0 1 1 1
0 1 0 0 0
1 1 0 0 1
Here's a nice URL for truth tables http://www.brian-borowski.com/Software/Truth/
Question 230567: help me slove this question . this is from california geomenrty book .
1.3.6.10.15 ...... what is the next pattern ? how did you slove it ?
please help me
thank you in advance
Answer by likaaka(51) (Show Source):
You can put this solution on YOUR website!1.3.6.10.15 ......
The answer is 21
You keep adding by the next sequential number
0 + 1 = 1
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
15 + 6 = 21
21 + 7 = 28, etc.
Question 230059: (PvQ)&(PvR) = Pv(Q&R)
cannot figure this out for the life of me
Answer by solver91311(6089) (Show Source):
You can put this solution on YOUR website!
It says that if P is true, then (P or Q) is true and so is (P or R), so the whole thing: [(P or Q) AND (P or R)] is true. But, if P is NOT true, then both Q and R have to be true so that (P or Q) will be true, (P or R) will be true and then the whole thing: [(P or Q) AND (P or R)] will be true.
John
Question 219061: What is an example for each of the laws of logic?
Answer by stanbon(29482) (Show Source):
Question 207907: I am lost on truth tables, can you please help?
Construct a truth table for ~q -->(~q ^ p)
Answer by jim_thompson5910(14863) (Show Source):
You can put this solution on YOUR website!To construct the truth table for ~q --> (~q ^ p), let's first break it up:
First, let's make a truth table for ~q:
Note: just write the opposite of q for every entry
Now, let's make a table for ~q ^ p (simply use the "and" operator for columns ~q and p):
| p | q | ~q | ~q ^ p | | T | T | F | F | | T | F | T | T | | F | T | F | F | | F | F | T | F |
Note: ~q ^ p is only true when both ~q and p are true. Otherwise, it's false.
Finally, make a table for ~q --> (~q ^ p):
| p | q | ~q | ~q ^ p | ~q --> (~q ^ p) | | T | T | F | F | T | | T | F | T | T | T | | F | T | F | F | T | | F | F | T | F | F |
Recall that p -> q is only false when p is true and q is false. Otherwise, it is true.
Question 202733: Rewrite ~ (p ~q) using DeMorgan's laws
Answer by jsmallt9(1023) (Show Source):
You can put this solution on YOUR website!The operator between p and ~q is not showing in my browser. So I am going to use "@" for the operator in the problem and "$" for the complementary operator. For example, if your operator is set union then "@" stands for this and "$" stands for set intersection.
According to DeMorgan's law
~(p @ ~q) = ~p $ ~~q = ~p $ q
Question 201378: I have been mulling over this problem for quite some time, and I think I have it right but I just need someone to look at it and confirm for me.
Here is the statement that I am presented with:
"If Verizon Wireless must remove installed equipment from a vehicle or fixed location in order to return it, then you will be charged a service fee."
My assignment requires me to put this in symbolic form and then create a truth table for it. Here is what I got.
p: Verizon Wireless must remove installed equipment from a vehicle
q: Verizon Wireless must remove installed equipment from a fixed location
r: You will be charged a service fee
In symbolic form: (p v q) --> r
and the truth table (in a weird format because of the text box, sorry):
p: T T T T F F F F
q: T T F F T T F F
r: T F T F T F T F
(p v q): T T T T T T F F
(p v q) -> r: T F T F T F T F
Any insight you can provide is much appreciated. Thank you in advance.
Answer by jim_thompson5910(14863) (Show Source):
You can put this solution on YOUR website!You have the correct symbolic translation, but normally you spell out EVERYTHING so you are perfectly clear. So the translation of "(p v q) --> r " would be:
"IF Verizon Wireless must remove installed equipment from a vehicle OR Verizon Wireless must remove installed equipment from a fixed location, THEN you will be charged a service fee"
Note: the underlined parts were cut and pasted from the given statements (so you can see that the statement is really "IF p OR q, THEN r" in symbolic form)
So here's the truth table:
| p | q | r | p v q | (p v q) -> r |
|---|
| T | T | T | T | T | | T | T | F | T | F | | T | F | T | T | T | | T | F | F | T | F | | F | T | T | T | T | | F | T | F | T | F | | F | F | T | F | T | | F | F | F | F | T |
Note: you'll normally see it in this format
If you aren't familiar with that format, then stick with your table. You did a good job with the table, BUT the last truth value in the bottom row should be T
p: T T T T F F F F
q: T T F F T T F F
r: T F T F T F T F
(p v q): T T T T T T F F
(p v q) -> r: T F T F T F T T
Question 201262: TWO PIPES FILL UP A TANK IN 9 3/8 HRS(75/8) . IF TWO PIPE RUN SEPARATELY THE LARGER DIA TAKES 10HRS LESS THAN THE SMALLER DIA PIPE TO FILL THE TANK INDIVIDUALLY . fIND THE NO OF HRS TAKE INDIVIDUAL TO FILL THE TANK ...
Answer by stanbon(29482) (Show Source):
You can put this solution on YOUR website!TWO PIPES FILL UP A TANK IN 9 3/8 HRS(75/8) . IF TWO PIPES RUN SEPARATELY THE LARGER DIA TAKES 10HRS LESS THAN THE SMALLER DIA PIPE TO FILL THE TANK INDIVIDUALLY . fIND THE NO OF HRS TAKE INDIVIDUAL TO FILL THE TANK ...
----------------------------------------------------
Together DATA:
time = (75/8) hrs/job ; rate = (8/75) job/hr.
------------------------------------------
Larger Pipe DATA:
time = x-10 hrs/job ; rate = 1/(x-10) job/hr.
--------------------------------
Smaller Pipe DATA:
time = x hrs/job ; rate = 1/x job/hr.
---------------------------------------------
Equations:
rate + rate = together data
1/x + 1/(x-10) = 8/75
---
75(x-10) + 75x = 8x(x-10)
75x - 750 + 75x = 8x^2 - 80x
8x^2 -230x + 750 = 0
4x^2 - 115x + 375 = 0
(x-25)(4x-15) = 0
Positive realistic solution.
x = 25 hrs. (time for the smaller pipe)
x-10 = 15 hrs. (time for the larger pipe)
==============================================
Cheers,
Stan H.
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Older solutions: 1..45, 46..90, 91..135
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