Tutors Answer Your Questions about sets-and-operations (FREE)
Question 565018: You were assigned a locker for your books at school. You forgot the locker number but remmeber that two of the 12 positive factors of the locker number are 6 and 25. What is your locker number? Show or explain how you got your answer.
Answer by KMST(592)   (Show Source):
You can put this solution on YOUR website!If two of the positive factors of the number are
 and  ,
the number must be a multiple of 
The number 150 has  positive factors.
Any other number who has 6 and 25 as factors will be a multiple of 150, and will have more than 12 factors.
So your locker is number 150.
How do I know has positive factors?
Because all the factors will be of the form
 where a and b could be 0 or 1, and c could be 0, 1, or 2.
That gives you 2 choices for a, 2 choices for b,and 3 choices for c. That makes combinations.
In case you don't believe, I'll list the factors of 150
 
 
 
 
 
 
Question 562097: what is 10t-3=t+15
Answer by Alan3354(21583)  (Show Source):
Question 561295: Numeration System and Sets
Explain how you would decide how to divide a school of 2080 students into sets?
50-100 words
thanks for all help
really makes a difference
Answer by jim_thompson5910(21667) (Show Source):
You can put this solution on YOUR website!You can divide them up by class, gender, height, age, social circle, etc to form many sets. For example, you could have one set be the set of all boys and the other be the set of all girls.
Question 558277: 1722.21 is 4.2 % of what number?
Answer by bluemockingjay7(41)  (Show Source):
Question 557271: Express the set in roster form. c = {x|x+3=44}
Answer by stanbon(48535) (Show Source):
You can put this solution on YOUR website!Express the set in roster form.
c = {x|x+3=44}
----
Since x+3 = 44 implies that x = 41,
---
c = {41}
===============
Cheers,
Stan H.
Question 551065: In a certain party each one of the group drinks coke or beer or whiskey or all. also 400 drink coke, 500 drink beer and 300 drink whiskey. 100 drink coke and beer, 200 drink beer and whiskey. 1 who drinks whiskey does not drink coke. how many are in the group?
Answer by Edwin McCravy(6935)  (Show Source):
You can put this solution on YOUR website!In a certain party each one of the group drinks coke or beer or whiskey or all. also 400 drink coke, 500 drink beer and 300 drink whiskey. 100 drink coke and beer, 200 drink beer and whiskey. 1 who drinks whiskey does not drink coke. how many are in the group?
There are 7 regions in the Venn diagram above
Circle C contains all the Coke drinkers, which are of 4 types:
Circle C is made up of 4 regions d,e,f, and h
Those in region d drink Coke but do not drink beer or whiskey
Those in region e drink Coke and beer, but do not drink whiskey.
Those in region h drink Coke, beer, and whiskey.
Those in region g drink Coke and whiskey, but do not drink beer.
Circle B contains all the beer drinkers, which are of 4 types:
Circle B is made up of 4 regions e,f,h, and i
Those in region e drink beer and Coke, but do not drink whiskey.
Those in region f drink beer, but do not drink coke or whiskey.
Those in region h drink beer, Coke, and whiskey.
Those in region i drink beer and whiskey, but do not drink Coke.
Circle W contains all the whiskey drinkers, which are of 4 types:
Circle W is made up of 4 regions g,h,i, and j
Those in region g drink whishey and Coke, but do not drink beer.
Those in region h drink whiskey, Coke, and beer.
Those in region i drink whiskey and beer, but do not drink Coke.
Those in region j drink whiskey, but do not drink Coke or beer.
Let's start with this clue:
>>...1 who drinks whiskey does not drink Coke. how many are in the group?
I take this to mean nobody drinks both Coke and whiskey. That
means there are nobody in regions g and h. So we put 0's there
>>...100 drink coke and beer...<<
So all 100 go in e since there are 0 in the middle. So we replace
e by 100
>>...200 drink beer and whiskey...<<
So all 200 go in i since there are 0 in the middle. So we replace
i by 200
>>...400 drink coke...<<
Three of the regions of circle C have 100, 0 and 0 in them.
So we have already accounted for 100 of the Coke-drinkers,
so the remaining 300 coke-drinkers are in region d. So we
replace d by 300:
>>...500 drink beer...<<
Three of the regions of circle B have 100, 0 and 200 in them.
So we have already accounted for 300 of the beer-drinkers,
so the remaining 200 beer-drinkers are in region f. So we
replace f by 200:
>>...300 drink whiskey...<<
Three of the regions of circle W have 0, 0 and 200 in them.
So we have already accounted for 200 of the whiskey-drinkers,
so the remaining 100 whiskey-drinkers are in region j. So we
replace j by 100:
Now we have all 7 regions filled with numbers, so
we add them up:
300+100+200+0+0+200+100 = 900
So there were 900 at the party. What a party!
Edwin
Question 478455: Use an Euler diagram to determine whether the syllogism is valid or invalid.
1.
All Cats have whiskers.
All things with whiskers are dogs.
[symbol] All cats are dogs.
Answer by nanpost1(1) (Show Source):
Question 549953: solve x=|1/2| + |-5/2|
Answer by josmiceli(6783)  (Show Source):
Question 549952: given the universal set E={1,2,3,4,5,6,7,8,9,10}
what is the complement of {1,10}
Answer by richard1234(4794)  (Show Source):
Question 549654: find f(g(x) and g(f(x)
a) f(x)= -3x ,g(x)=2x+6
b) f(x)= x^2 + 4x , g(x)= x-1
Answer by mathie123(175) (Show Source):
You can put this solution on YOUR website!a) f(x)= -3x ,g(x)=2x+6
f(g(x)) is just basically saying everywhere you have an x in f(x), put the entire g(x) function.
So for this example, f(g(x))=-3(2x+6)
and g(f(x)) is just saying everywhere you have and x in g(x), put the entire f(x) function
So for this example, g(f(x))=2(-3x)+6
I will let you do b) yourself (hint: VERY similar to a), just different functions.
_____________________________________________________________________
Hopefully this helps! Let me know if you are still unsure
Romans 5:8
Question 517801: Could you express the following set in set-builder notation?
B={4,5,6,7,8,9,10,11}
Answer by solver91311(12126)  (Show Source):
Question 517668: A={3x: x ∈ N}
B={x+7: x ∈ N)
C={3x+21: x∈ N)
Prove AnB⊆C and C⊆AnB. (n=intersect). If false explain why it does not hold.
Answer by Gogonati(762)  (Show Source):
You can put this solution on YOUR website!A≴B, A∐B, A∎B, x∌y, x∉y, x∈y, x∇y
x∆y, x∅y, xℹy, x↢y, x≪y, x≥y, x≦y
x≧y, x≨y, x≩y, x≪y, x≫y, x≬y, x≭y
x≡y, x≢y, x≣y, x≤y, x⇼y, x∁y, x⇿y
xy, xϩy, xߑy, xಌy, xᇊy, xᎉy, xᖩy
x᪔y, xṽy, xṺy, xṼy, xṾy, xṿy, xờy
xὁy, xᾩy, x y, xy, ab, xy, xy
x∃y, x∂y, x∄y, x∅y, x∈y, x∉y, x∊y
x∋y, x∌y, x∍y, x∎y, x∏y, x∐y, x∑y
∑B
Question 515089: Hello, I am having trouble with this problem
Find the N(A) for the set
700,701,702,.....,7000
Answer by richard1234(4794) (Show Source):
You can put this solution on YOUR website!Subtract 699 from each element (this does not change the cardinality of the set).
1,2,3,...,6301
Hence the cardinality, or n(A), is 6301.
Question 511628: one number is 3 times another number. Find the numbers if the sum of their reciprocal is 1.
Found 2 solutions by josmiceli, oberobic:
Answer by josmiceli(6783) (Show Source):
Answer by oberobic(2302) (Show Source):
You can put this solution on YOUR website!
.
.
.
Multiply through by 3y
.
.
.
.
.
Check the sum of reciprocals.
.
Correct.
.
Answer: One number is 4/3 and the other is 4.
.
Done.
Question 510299: There are a total of 108 foreign language students in a high school where they offer Spanish, French, and German.
There are 21 students who take at least 2 languages at once.
If there are
44 students of Spanish,
45 students of French, and
40 students of German,
how many students take all three languages at once?
Answer by edjones(7311)  (Show Source):
You can put this solution on YOUR website!Let 21 take spanish and french.
Then 44-21=23 take only spanish.
45-21=24 take only french.
40 take only German.
21+23+24+40=108
None take all 3 languages.
.
Ed
Question 500817: 1. Whenever we encounter a new proposition, it is a good idea to explore the
proposition by looking at specific examples. For example, let
a =20, b = 12, and t = 4. In this case, t given a and t given b. In each of
the following cases, determine the value of (ax + by) and determine if t
divides (ax + by).
(a) x = 1; y = 1 a. yes
(b) x = 1; y = -1 b. yes
(c) x = 2; y = 2 c. yes
(d) x = 2; y= -3 d. yes
(e) x = -2; y = 3 e. yes
(f) x = -2; y = -5 f. yes
2. Repeat Part (1) with a = 21, b = -6, and t =3.
a. yes d. yes
b. yes e. yes
c. yes f. yes
3. We started the forward-backward process for the proof of Proposition 4.15
following the discussion of this proposition. Complete the following proof
of Proposition 4.15.
Proposition 4.15. Let a, b, and t be integers with t ≠ 0. If t divides a and t
divides b, then for all integers x and y, t divides ax + by.
Proof. Let a, b, and t be integers with t ≠ 0, and assume that t divides a and
t divides b. We will prove that for all integers x and y, t divides (ax + by).
So let x is an element of Z and let y is an element of Z. Since t divides a, there exists an integer m such that ….
Answer by richard1234(4794) (Show Source):
You can put this solution on YOUR website!Pretty straightforward. If t divides a and t divides b, then a ≡ 0 (mod t) and b ≡ 0 (mod t). Then we can multiply a and b by integers and the residue is still 0 mod t (i.e. ax ≡ 0, by ≡ 0). Then we can add them and we obtain our desired result, ax + by ≡ 0 (mod t) <--> t divides ax + by.
Question 500690: One of the most famous unsolved problems in mathematics is a conjecture
made by Christian Goldbach in a letter to Leonhard Euler in 1742. The
conjecture made in this letter is now known as Goldbach’s Conjecture. The
conjecture is as follows:
Every even integer greater than 2 can be expressed as the sum of two
(not necessarily distinct) prime numbers.
Currently, it is not known if this conjecture is true or false, although most
mathematicians believe it to be true.
(a) Describe one way to prove that Goldbach’s Conjecture is false.
(b) Prove the following:
If there exists an odd integer greater than 5 that is not the sum of
three prime numbers, then Goldbach’s Conjecture is false.
Answer by solver91311(12126) (Show Source):
Question 495875: It was stated that a real function is a function whose domain
and codomain are subsets of the real numbers R. Most of the functions
used in calculus are real functions. Quite often, a real function is given by a
formula or a graph with no specific reference to the domain or the codomain.
In these cases, the usual convention is to assume that the domain of the real
function f is the set of all real numbers x for which f(x) is a real number and that the codomain is R. For example, if we define the (real) function f
by,
f(x)=x/x-2,
we would be assuming that the domain is the set of all real numbers that are not equal to 2.
Determine the domain and range of each of he following real functions.
a.)The function k defined by k(x)=the square root x-3
b.)The function F defined by F(x)=In(2x-1)
c.)The function f defined by f(x)=3 sin(2x)
d.)The function g defined by g(x)=4/x^2 - 4
Answer by richard1234(4794) (Show Source):
You can put this solution on YOUR website!Simply find the set of all possible x-values, and the set of all possible y-values. For example,
 = \sqrt{x-3})
is not defined on real numbers if x < 3. Also, the range of k(x) is [0, infinity) because the square root of any real number is nonnegative.
Try the others the same way.
Question 490329: Find a counterexample to show that the following statement is false:
The sum of twi-digit numbers is a three-digit number.
__ + __ is a two-digit number.
Answer by Alan3354(21583) (Show Source):
Question 489859: How would you write the following set using set builder notation: B={3,7,11,15,19}.
Answer by stanbon(48535) (Show Source):
You can put this solution on YOUR website!How would you write the following set using set builder notation: B={3,7,11,15,19}.
-----------
B = {3 + 4x| x = 0,1,2,3.4}
============================
Cheers,
Stan H.
Question 484526: I'm having a problem with this set. The question is..
Prior to the 7:15 show at the local movie theater, 70 people visited the concession stand, Listed below is what they ordered
42 ordered popcorn
18 ordered candy
30 ordered a soda
10 ordered popcorn and candy
8 ordered soda and candy
12 ordered popcorn and soda
5 ordered popcorn, candy and soda
1. How many people ordered something other than popcorn, candy or soda?
2. How many people ordered popcorn and a soda but not candy?
3. How many people ordered candy or a soda but not popcorn?
4. How many people ordered popcorn or candy?
Answer by solver91311(12126) (Show Source):
You can put this solution on YOUR website!
Draw a large rectangle. Inside of the rectangle draw three circles that partially overlap.
Label the circles P, C, and S.
In the very center where the three circles overlap, that is to say the one region on your diagram where you are inside of all three circles, put the number 5 representing the 5 people who ordered P, C, AND S.
The region where P and C overlap needs to contain the number of people who ordered ONLY P and C. The number 10 given for people who ordered P and C also includes those who ordered P, C, and S. So from the given 10 subtract those that ordered all three, that is 10 minus 5 = 5. And you put 5 into the P and C only region. Similarly, since 12 minus 5 equals 7, you put 7 in the P & S only region. Then, since the number who ordered P includes those who ordered P & C, those who ordered P & S, AND those who ordered all three, add up 5 plus 7 plus 5 = 17, then subtract 17 from the 42 we are told ordered P to arrive at 25 who ordered ONLY P. Use similar logic to fill in the rest of your diagram.
Next add all of the numbers that you have entered in your diagram. Subtract that result from 70, the number of people surveyed, to get the number of people who did not order P, S, OR C. Several of us only wanted ice cream. Write that number in the rectangle outside of all of the circles.
You should be able to answer all of the questions posed just from the data in your diagram.
John
My calculator said it, I believe it, that settles it
Question 482658: Problem says this, and it is a multiple choice question:
Given the following sets, select the statement below that is NOT true.
A = {b, l, a, z, e, r}
B = {b, a, l, e}
C = {a, b, l, e}
D = {l, a, b}
E = {a, b, l}
Multiple choice possibilities:
1. E ⊂ A
2. C ⊂ A
3. D ⊆ B
4. C ⊂ B
5. D ⊂ A
Could someone help me with this, please? Thank you.
Answer by Edwin McCravy(6935) (Show Source):
You can put this solution on YOUR website!
Problem says this, and it is a multiple choice question:
Given the following sets, select the statement below that is NOT true.
A = {b, l, a, z, e, r}
B = {b, a, l, e}
C = {a, b, l, e}
D = {l, a, b}
E = {a, b, l}
You need to learn the difference betweeen ⊂ and ⊆.
It's like the difference between < and ≤. A line under either symbol
means "EQUALITY IS ALLOWED BUT NOT REQUIRED", When there is no line
underneath, it means "EQUALITY IS NOT ALLOWED".
Multiple choice possibilities:
1. E ⊂ A, TRUE because "a,b,&l" are all part of but not all of "b,l,a,z,&e"
2. C ⊂ A, TRUE because "a,b,l,&e" are all part of but not all of "b,l,a,z,&e
3. D ⊆ B, TRUE because "l,a,&b" is part of or all of "b,a,l,&e".
4. C ⊂ B, FALSE because "a,b,l,&e" is ALL OF, not just part of "b,a,l,&e"
5. D ⊂ A, TRUE because "l,a,&b" are all part of but not all of "b,l,a,z,&e"
Edwin
Question 482196: The problem says this:
Are the two sets equal, equivalent, neither or both?
V = {eye, nose, ear, mouth, tongue}; W = {tongue, ear, mouth, eye, nose}
Will someone help me with this? Also, to get a better understanding of this, would you mind explaining your answer? Thank you so much!
Found 2 solutions by MathLover1, stanbon:
Answer by MathLover1(3376)  (Show Source):
You can put this solution on YOUR website!They are   and  .
Rearranging the elements in a different order between the braces does not change the set.
by definition:
Two sets are if their  is .
The cardinality of a set is the number of elements in the set.
The cardinality of V is  and the
The cardinality of W is . So the sets are .
Two sets are if the two sets consist of the    .
Set  and set   the same elements.
Answer by stanbon(48535) (Show Source):
You can put this solution on YOUR website!Are the two sets equal, equivalent, neither or both?
V = {eye, nose, ear, mouth, tongue}; W = {tongue, ear, mouth, eye, nose}
---
V and W are equal.
They have the same elements: no more and no less.
----
Equivalent sets have the same number of elements
but not the same elements.
---
Cheers,
Stan H.
Question 482202: Problem says this:
Given
U = {15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}
A = {16, 18, 20, 22}
B = {17, 19, 20, 23, 24}
Find A′∩ B′.
Could you please help me with this? Thank you so much!
Answer by stanbon(48535) (Show Source):
You can put this solution on YOUR website!U = {15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}
A = {16, 18, 20, 22}
B = {17, 19, 20, 23, 24}
Find A′∩ B′.
----
A' = {15,17,19,21,23,24,25}
B' = {15,16,18,21,22,25}
----
A' AND B' = {15,21,25}
=========================
Cheers,
Stan H.
================
Question 482194: Problem says:
Express the following in roster form: Set M is the set of natural numbers between seventeen and twenty-three.
Could someone help me with this, please? Thank you so much.
Answer by stanbon(48535) (Show Source):
You can put this solution on YOUR website!Express the following in roster form: Set M is the set of natural numbers between seventeen and twenty-three.
-------------------------
M = {18,19,20,21,22}
================
Cheers,
Stan H.
Question 481414: The problem says this:
Find P ∩ Q. Write in correct set notation.
The diagram:
http://www.flickr.com/photos/62474130@N03/6040495154/
Could you help me with please? Thank you.
Answer by mananth(10548)  (Show Source):
Question 481352: The problem says this, and it is multiple choice:
Given the following sets, select the statement below that is true.
A = {b, l, a, z, e, r}, B = {b, a, l, e}, C = {a, b, l, e}, D = {l, a, b}, E = {l, a}
1. E ⊆ A and B ⊂ C
2. C ⊂ D and E ⊂ C
3. D ⊆ C and D ⊆ E
4. C ⊂ E and B ⊆ A
5. D ⊂ C and B ⊆ C
Can you help me with this please? Thank you so much!
Answer by Theo(2967)  (Show Source):
You can put this solution on YOUR website!⊆ means improper subset
⊂ means proper subset
an improper subset means that A is a subset of B, but B doesn't contain any elements in it other than the elements that are also in A.
an example would be:
A = {a,b,c,d}
B = {a,b,c,d}
these sets are identical so:
A ⊆ B and B ⊆ A are valid.
a proper subset means that A is a subset of B, but B contains additional elements that are not in A.
an example would be:
A = {a,b,c}
B = {a,b,c,d}
A ⊂ B is valid.
B ⊂ A is not valid.
All elememnts in A are in B, but B contains additional elements not in A, namely d.
here's a reference from the web that explains it as well.
http://answers.yahoo.com/question/index?qid=20080125081016AA94Fwe
i analyzed each of your statements in turn and found the following:
1. E ⊆ A and B ⊂ C
E is a proper subset of A because it has less elements than A.
B is an improper subset of C because they both contain the same elements.
This answer is not correct.
2. C ⊂ D and E ⊂ C
C cannot be a subset of D because D contains fewer elements than C.
if anything, it would be the other way around.
D ⊂ C would be more appropriate.
3. D ⊆ C and D ⊆ E
D is a proper subset of C, not an improper subset.
Also D is not a subset of E because E contains fewer elements than D.
4. C ⊂ E and B ⊆ A
C is not a subset of E because E contains fewer elements than C.
5. D ⊂ C and B ⊆ C
D is a proper subset of C because D contains fewer elements than C.
B is an improper subset of C because they both contain the same elements.
THIS ONE LOOKS CORRECT !!!!!
I believe your answer is selection 5.
D contains {b,l,a}
C contains {b,l,a,e}
B contains {b,l,a,e}
it does help to reorder the terms so you can see the relationships easier.
you can see that B and C are identical sets, so B ⊆ C is correct.
you can see that all elements in D are also in C and that D contains fewer elements than C, so D ⊂ C is correct.
I'd go with selection 5.
Question 481009: Can someone help me with this please?
My Problem says this:
Determine the following: A ∪ B′
Let
U = {1, 2, 3, 4, 5, 6, 7, 8}
A = {1, 2, 4, 5, 8}
B = {2, 3, 4, 6}
The photo:
http://www.flickr.com/photos/62474130@N03/6036660666/
Answer by solver91311(12126) (Show Source):
You can put this solution on YOUR website!
B' is everything that is in U but not in B. A ∪ B' is everything that is either in A, in B', or in both.
John
My calculator said it, I believe it, that settles it
Question 481008: My problem says this:
Use the graph to represent each set in roster form. The set of years included in the graph in which digital camera sales were less than 6 million.
Can someone please help me with this?
Here is the graph:
http://www.flickr.com/photos/62474130@N03/6036660664/
Answer by solver91311(12126) (Show Source):
You can put this solution on YOUR website!
There is a set of numbers across the bottom of your graph. Those represent years. There is a set of numbers at the top of each bar on the graph. Inside of a pair of braces, list the years where the number at the top of the bar is smaller than 6.
John
My calculator said it, I believe it, that settles it
Question 480845: In Exercises 25-32, determine whether A = B, A ⊆ B, B ⊆ A, A ⊂ B, B ⊂ A or if none of these answers applies.
A = {x | x is a sport that uses a ball} B = {basketball, soccer, tennis)
Answer by Theo(2967) (Show Source):
You can put this solution on YOUR website!B would be a subset of A because:
A is the set of all sports that use a ball.
B is the set of sports that are either basketball, soccer, or tennis.
since all of these sports use a ball, B is a subset of A.
since A can include sports other than basketball, soccer, or tennis (football for example), then B is a proper subset of A.
your answer should be:
B ⊂ A
Question 480571: PERMUTATIONS AND COMBINATIONS
A CLUB CONSISTS OF 16 MEN AND 19 WOMEN. IN HOW MANY WAYS CAN THEY CHOOSE A PRESIDENT, VICE PRESIDENT, TREASURER, AND SECRETARY, ALONG WITH AN ADVISORY COMMITTEE OF SIX PEOPLE? (ROUND THE ANSWER TO FIVE DECIMAL PLACES.)
Answer by solver91311(12126) (Show Source):
Question 480509: Determine whether A = B, A ⊆ B, B ⊆ A, A ⊂ B, B ⊂ A or if none of these answers applies.
A = {x | x is a sport that uses a ball}
B = {basketball, soccer, tennis}
Answer by Edwin McCravy(6935) (Show Source):
You can put this solution on YOUR website!Determine whether A = B, A ⊆ B, B ⊆ A, A ⊂ B, B ⊂ A or if none of these answers applies.
A = {x | x is a sport that uses a ball}
B = {basketball, soccer, tennis}
A = B No A doesn't equal B because for instance, A contains baseball, golf,
etc. but B doesn't.
A ⊆ B No, every element of A is not an element of B because for
instance, baseball is an element of A,
B ⊆ A Yes because, although B doesn't equal A by any means, every
element of B is also an element of A.
A ⊂ B No, this is just like A ⊆ B except that A ⊆ B allows
but does not require, the possibility of A = B, whereas A ⊂ B doesn't
allow A = B. But that's not any worry here.
B ⊂ A Yes because every element of B is also an element of A. The only
difference between ⊂ and ⊆ is that ⊂ does NOT allow the sets
on both sides of it to be exactly the same set, whereas ⊆ allows it but
does not require it.
So B ⊆ A and B ⊂ A are the only ones that hold.
Examples:
{a,r,t} = {t,a,r} is true because the order they're listed in doesn't matter
{a,r,t} ⊆ {t,a,r} is true because ⊆ allows (but doesn't require)
equality
{a,r,t} ⊂ {t,a,r} is false because ⊂ does not allow equality
{a,r,t} ⊂ {s,t,a,r} is true because every element of the left set is also
an element of the right set. It doesn't allow equality but we surely don't
have that.
{a,r,t} ⊆ {s,t,a,r} is true because every element of the left set is also
an element of the right set. It allows equality but doesn't require it.
Edwin
Question 479270: I need to construct a truth table. (p "and" ~q)--q
Answer by Theo(2967) (Show Source):
You can put this solution on YOUR website!here's your truth table.
p q ~q (p^~q) (p^~q)->q (p^~q)<->q
T T F F T F
T F T T F F
F T F F T F
F F T F T T
if q is true, then ~q is false.
if q is false, then ~q is true.
(p^~q) is only true if both p and ~q are true,otherwise it's false.
(p^~q)->q is only false if (p^~q) if True and q is false.
(p^!q)<->q is only True if both are True and if both are false. If they are mixed (TF or FT), then it's false.
A->B means that A implies B which states that "if A is true, then B is true".
A<->B means that A is equivalent to B which means that "if A is true, then B is true and if B is true, then A is true". This is also stated as "A is true if and only if B is true".
Question 475954: for each given set,how do I choose the set with the same cardinality
{1,4,7,...,91,94}
{1,2,3,...,205,206}
{1,3,5,...,211,213}
possible choices {147,148,149,...,240}{131,132,133,...,247} {3,4,5,...,34} {1423,1425,1427,...1833}
Answer by richard1234(4794) (Show Source):
You can put this solution on YOUR website!There are two ways to find the cardinality of this set. You can either use the formula for an arithmetic sequence a_n = a_1 + (n-1)d, but I prefer finding the cardinality by doing a series of transformations on the set. For example, with the set {1,4,7,...,94} we can add 2 to each element (this will not affect cardinality) to get {3,6,...,96}, then divide each element by 3 to get {1,2,...,32} which obviously has 32 elements.
Question 475946: for each given set,how do I choose the set with the same cardinality
{1,4,7,...,91,94} Possible choices
{1,2,3,...,205,206} {131,132,133,...,247}
{1,3,5,...,211,213} {147,148,149,...,240}
{3,4,5,...34}
{131,132,133,...,237}
{1423,1425,1427,...,1833}
Answer by tinbar(122) (Show Source):
You can put this solution on YOUR website!By the given patterns, you should be able to determine the size of each set.
For example: the size of {1,2,3,...,205,206} is obviously 206.
So you need to figure out the sizes of all sets including {1,4,7,...,91,94}, {1423, 1425, 1427,...,1833} and {1,3,5,...,211,213} which are the hardest ones.
To do them, here's a hint, consider the formula for the general term of an arithmetic sequence: a(n) = a(1) + (n-1)*d, which basically says that the nth term of the sequence is the first term plus the difference times the amount of terms that already exist, namely (n-1), and of course the difference is the difference between the successive terms.
For {1,4,7,...,91,94} we have the first term equal to 1, and the last term is 94, the common difference between each successive term is 3, so now we can work backwards to figure out which numbered term 94 is. Once we do this, we essentially have the size of the set. We know the formula given above must hold, therefore 94=1+(n-1)*3...(I'll let you do the algebra here and just give the answer, but you should check and make sure you come to the same conclusion in order to determine the sizes of the other sets)...we get n = 32. So therefore, we have the size of this set as 32.
So now you have to find another set with size 32 and that's the set your looking for.
Good Luck!
Question 475929: how do I perform the given operations. (Enter solutions from smallest to largest) If there are any unused answer boxes, enter none in the last boxes.
{17,22,26} u {22,17,37}
{17,22,26} n {22,17,37}
{17,47,26} u {92,80,37}
{17,47,26} n {92,80,37}
Answer by stanbon(48535) (Show Source):
You can put this solution on YOUR website!{17,22,26} u {22,17,37} = {17,22,26,37}
-------------------------------------------
{17,22,26} n {22,17,37} = {17,22}
-------------------------------------------
{17,47,26} u {92,80,37} = {17,26,37,47,80,92}
-------------------------------------------
{17,47,26} n {92,80,37} = empty set
=====================================
Cheers,
Stan H.
Question 472805: Given that U = {students in a college},
A = {students who are over 180 cm tall},
B = {students who are vegetarian},
C = {students who are cyclists},
express in words each of the following
i) A∩B ≠ Ø
ii) A ⊂ C'
Express in set notation the statement
(iii) all students who are both vegetarians and cyclists are not over 180 cm tall.
Answer by solver91311(12126) (Show Source):
You can put this solution on YOUR website!
i) There exist students at the college who are both over 180 cm tall and who are vegetarians.
ii) All of the students who are over 180 cm tall are not cyclists.
iii) \ \subset\ A')
John
My calculator said it, I believe it, that settles it
Question 472115: A long distance phone call cost 36 cents for the first three minutes and 11 cents for each additional minutes. How long can you talk for less than $2
Answer by jorel1380(2518)  (Show Source):
Question 470742: Construct a truth table for ( ~p disjunction ~ q )conditional p.
Please show the steps on how you did this
Answer by MathLover1(3376) (Show Source):
You can put this solution on YOUR website!
Construct a truth table for ( ~p disjunction ~ q )conditional p
A disjunction asserts that at least one of two statements is true.
The two statements are called the disjuncts of the disjunction. The
disjunction is represented by the symbol 'v' which reads 'or'.
CONDITIONALS
A conditional asserts that one statement is true if another
statement is true. It is typically expressed by "if ... then ...", but it
does not carry all the conotations that "if ... then ..." usually carries.
(P => Q)
so, you have:
( ~p v ~ q )=> p
here is your table:
http://imageshack.us/photo/my-images/849/capture715201192636pm.jpg/
Question 470750: Fill in the heading of the following truth table
p q ?
T T T
T F T
F T T
F F F what should the third column be
Answer by MathLover1(3376) (Show Source):
Question 470508: Using correct mathematical notation and symbols, express the following in set-builder notation: Z = {17, 18, 19, 20, 21, 22, 23, 24, 25}
Answer by stanbon(48535) (Show Source):
You can put this solution on YOUR website!Using correct mathematical notation and symbols, express the following in set-builder notation: Z = {17, 18, 19, 20, 21, 22, 23, 24, 25}
----------
{x | 17 <= x <= 25,x E Integers|
=============================
Cheers,
Stan H.
Question 468967: Given U = {10,11,12,13,14,15,16,17,18,19,20}, A= {11,13,15,19}, & B= {10,12,14,15,16,19}.
Find A' union B' Show all work on finding A', then B' then the union
Answer by Edwin McCravy(6935) (Show Source):
You can put this solution on YOUR website!given U={10,11,12,13,14,15,16,17,18,19,20}, A={11,13,15,19} & B={10,12,14,15,16,19}
find A' ᑌ B' Show all work on finding A', then B' then the union
A' is the set of all elements of U that are not elements of A,
so A' = {10,12,14,16,17,18,20}.
B' is the set of all elements of U that are not elements of B,
so B' = {11,13,17,18,20}.
Therefore
A' ᑌ B' = {10,12,14,16,17,18,20} ᑌ {11,13,17,18,20}
ᑌ means to get the set of all those elements that are in
the sets on both sides of the symbol ᑌ, whether they are
in common or not.
A' ᑌ B' = {10,11,12,13,14,16,17,18,20}
Edwin
Question 468991: Someone Please help me!
Given the following A={1,2,3} B={1,2,3,4,5} and C= {4,5,6,7} Evaluate each set
a) A intersection B
b) A union C
c) B union C
d) (A union B)intersection C
e) A union (B union C)
f) (A intersection B) intersection C
g) (A intersection B)union C
Answer by MathLover1(3376) (Show Source):
You can put this solution on YOUR website!
Given; A={1,2,3} B={1,2,3,4,5} and C= {4,5,6,7}
a) A intersection B
The INTERSECTION of two sets is the set of elements which are in both sets.
A intersection B={1,2,3}
b) A union C
The UNION of two sets is the set of elements which are in either set.
A union C={1,2,3,4,5,6,7}
c) B union C={1,2,3,4,5,6,7}
d) (A union B)intersection C={1,2,3,4,5}intersection {4,5,6,7}={4,5}
e) A union (B union C)= {1,2,3} union {1,2,3,4,5,6,7}={1,2,3,4,5,6,7}
f) (A intersection B) intersection C={1,2,3} intersection {4,5,6,7}={ }
g) (A intersection B)union C={1,2,3} union {4,5,6,7}={1,2,3,4,5,6,7}
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225
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