Questions on Logic: Propositions, Conjunction, Disjunction, Implication answered by real tutors!

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Question 4140: what is the meaning of conditional statement. what is the two parts of it and also can you please define "converse" and "inverse". please also define the following:
1. contrapositive
2. tauthology
3. contradiction
4. logical equivalence

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Question 49918: Simplifying a product of radical expressions.
(2 square root of 3-3 square root of 10) (6 square root 10-3 square root of 3)
3x+3x+9xyz=z

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Question 53566: " I have been having trouble figuring this out. I have been on it for a while now but I is just not coming to me."
p:spuare root of nsegative 64 = 8
q: An equilateral triangle has three congruent sides.
r:0<0
s: An obtuse angle measures greater than 90 degrees and less than 180 degrees.
18.) p and q
20.) p and r
22.) r and s
24.)p ^ s
Instructions: Use the following statements to write a compound statement for each conjunction and disjunction. Then find its truth value.

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Question 76567: Given: (~ p → q) ∨ ~ p
This statement is a:
A. Biconditional statement B. Self-Contradiction
C. Tautology D. Conjunction

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Question 76566: assume P = FALSE, Q = TRUE, and R = FALSE.
Determine the truth of the following statements.
Problem [q → ~ (r ∨ p)]↔ (p → ~ r )
A. True B. False
Problem (~ r ∨ ~ q) ∧ (~ p → r )
A. True B. False

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Question 80835: Construct a truth table and determine how many cases are TRUE
Given: (R v Q) --> P
A. 4
B. 5
C. 7
D. All cases are TRUE

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Question 87460: If the remote control is not within my reach, then I will watch the same channel all night.
I need the converse, inverse for the sentences.
I came up with for the contrapositive: If you do not watch the same channel all night, then the remote control is not within my reach.
Is this correct?

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Question 88960: P is True, q and r are False- find the truth value.
a) (p ^ ~q) ^ r


b) ~(q ~ r)

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Question 88948: Let p represent a true statement, while q and r represent false statements. Fing the truth value of the compound statement.
a) (p^~q) ^ r
b) ~(q v ~r)

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Question 92539: Find the distance between each pair of points.
(-3,0) and (4,0)

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Question 114116: How would this be translated?
Tulane increasing enrollment is a necessary condition for Duke’s reducing class size if and only if Fordham’s raising tuition is a sufficient condition for Georgetown’s expanding course offerings.

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Question 117517: I can't help my daughter answer this:
Use p and q to find the truth value of the compound statement p ^ q
p: blue is a color
q: the sum of the measures of the angles of a triangle is 160 degrees.

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Question 117517: I can't help my daughter answer this:
Use p and q to find the truth value of the compound statement p ^ q
p: blue is a color
q: the sum of the measures of the angles of a triangle is 160 degrees.

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Question 123503: Given a conditional statement p --> q, find the inverse of its inverse, the inverse of its converse, and the inverse of its contrapositive.
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Question 134540: ues the 45-45-90 right triangle Conjucture to find the lenths of each triangle
a=5,b=__, c=__

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Question 136137: Can you help me. I need to how to do this logic problem, step by step.
Three geniuses stand in a file (one behind the other). Each can see only to the front, so the rear person can see the middle and the front, the middle person can see the front, and the genius in the front cannot see anyone.
You have five hats. Two are white, and three are red. You blindfold the three geniuses, who are utterly truthful, and put a hat – at random – on the head of each. Then you hide the other two hats and remove the blindfolds.
You then ask each genius to name the color of his hat (which he cannot see).
The rear one says "I don't know." The middle on says, "I don't know." Then the front one says, "I know."


WHAT COLOR IS THE FRONT GENIUS' HAT??????

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Question 138666: Determine which, if any, of the three statements are equivalent.
a) If today is Monday, then tomorrow is not Wednesday
b) It is false that today is Monday and tomorrow is not Wednesday
c) Today is not Monday or tomorrow is Wednesday
My answer is none of the statements are equivalent. The reason for this is that"a" and "b" are not equivalent, "a" and "c" are not equivalent, and "b" and "c" are not equivalent. I referred to DeMorgan's Laws.

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Question 138668: ) Determine the truth value of the following statement:
Rembrandt was a famous painter and some odd numbers are prime.
p: Rembrandt was a famous painter
q: Some odd numbers are prime.
(It is known that prime numbers are odd, however, not all prime numbers are odd; for example 21 factors out to 1 * 27 and 3 * 7)
p q p ^ q
T T T
T F F
F T F
F F F
Both p and q must be true in order for the statement to be true.
Answer: the statement is true.

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Question 143732: I am having a lot of trouble with word problem questions. If someone could help me that would be great. If you could show your work so that I can understand how you got the answer would be apprectiated. Thanks so much!
7. (4 pts) Use an Euler diagram to determine whether the syllogism is valid or invalid
All actresses are beautiful
Some actresses are tall
--------------------------------
; Some beautiful people are tall.

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Question 143728: I am having a lot of trouble with word problem questions. If someone could help me that would be great. If you could show your work so that I can understand how you got the answer would be apprectiated. Thanks so much!
5. (2 pts) Rewrite ~(pVq) using DeMorgan's laws.

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Question 143812: I am having a lot of trouble with word problem questions. If someone could help me that would be great. If you could show your work so that I can understand how you got the answer would be apprectiated. Thanks so much!
8. (6 pts) Construct a truth table for (qp)  q
Symbols copied as squares so: 1st square is a ~ , 2nd square is /\(v reversed), 3rd square is arrow pointing to right, 4th square is ~

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Question 144001: Could you help me?
Construct a truth table for ~ (p v q)

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Question 144082: I am having trouble again. Can you helo me solve this
Let p, q, and r be the following statements:
p: Mike is sailing
q: Alice is on vacation
r: Sam is in town
Translate the following statement into English: (p v ~ q) Arrow ~r

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Question 144080: I really need some help. Will you help me solve this?
Write the following compound statement in symbolic form
Let p: Today is Monday
q: Tomorrow is the day Sara leaves
If tomorrow is not the day Sara leaves, then today is Monday

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Question 144079: Can you please help me?
Write the negation for the statement below.
No one in the family eats rhubarb

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Question 144085: HELP
Determine the truth value of the statement ~q arrow [ ~ r v (revered) (p v q)] when p is false, q is true, and r is true.

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Question 144084: Can you help me
Use Euler Diagrams to determine whether the following syllogism is valid or invalid.
Some senators are conservationists
No conservationists are pro-development
--------------------------------------------------
 Some senators are not pro-development

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Question 144083: Need help again-thx
Write the converse, inverse, and contrapositive of the following conditional statement
If a dog is barking, then it will not bite

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Question 148558: a) Translate the argument into symbolic form and (b) determine if the argument is valid or invalid. You may compare the argument to a standard form or use a truth table.
If Lillian passes the bar exam, then she will practice law.
Lillian will not practice law
----------------------------------------------------------------------
 Lillian did not pass the bar exam

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Question 148796: Can I please get some help with this.

4 pts) For each of the following conditionals, identify the antecedent and the consequent. Form the converse, inverse, and contrapositive.
(a) If I don’t go to the movie, I’ll study my math.
(b) Your car won’t start if you don’t have gasoline in the tank.

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Question 148838: Can someone please help me?

4. (4 pts) Construct a truth table for  (p  q)
Its the squiggle symbol meaning NOT(p v q)

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Question 148842: Can you please help me?
10. (3 pts) Use De Morgan’s Laws to determine whether the two statements are equivalent
NOT (p AND q), NOT (q Or NOTp)

you understand what im saying right?

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Question 148844: Can someone please help me?

5 pts) Determine whether the argument is valid or invalid.

A tree has green leaves or the tree does not produce oxygen.
This tree has green leaves
------------------------------------------------------------------------
 This tree does not produce oxygen.
.
the square has actually. . this symbol

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Question 151900: (1)proof that the contrapositive of the statement is logically equivalant to the statement.
(2)Proof also that the converse statement is logically equivalant to the inverse of the statement.

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Question 167024: It is w or D
It is D
Conclusion equals W or ~W?

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Question 179406: what is a real life example of a tautology?
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Question 184165: write the converse, inverse and, contrapositive of the folowing. If we have a rock concert, someone will faint.

I have no Ideas about this can you help please

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Question 185357: Fill the headings of the following truth table using p, q, ~, ->, v, and ^.
p q (a) (b)
______________________________
T T T F
T F T F
F T T F
F F F T

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Question 185356: Let p, q, and r be the following statements:
p: Roses are red
q: The sky is blue
r: The grass is green
Translate the following statements into English
(a) p ^ q (b) p ^ (q v r) (c)q -> (p ^r) (d) ( ~ r ^ ~ q) -> ~ p

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Question 185647: Construct a truth table for (~q^p) -> ~q

Can you please assist me wit this, i don't even know where to start.

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Question 185765: I am actually getting myself confused here: Please Help!
a.) If today is Monday, then tomorrow is not Wednesday.
b.) If it is false that today is Monday and tomorrow is not Wednesday
c.) Today is not Monday or tomorrow is Wednesday.
I personally would say that A & B are equivalent, but the more I read over it and convince myself that A & B are equivalent, the more I confuse myself. Can you please help me determine which statements are equivalent. Thanks A million everyone

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Question 185877: Write the following compound statement in symbolic form
Let p: Today is Monday
q: Tomorrow is the day Sara leaves
If tomorrow is not the day Sara leaves, then today is Monday

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Question 192749: Here is the 2nd question I mentioned. It is from an homework assignment. We are studying the text Survey of Mathematics w/Applications. I just can't seem to follow the logic of these questions. Pleae help!
Here is the question:
5.(2 pts) Rewrite ~ (p v ~q) using DeMorgan's laws.

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Question 192771: For each of the following conditionals, identify the antecedent an the consequent. Form the converse,inverse,and contrapositive.
a. If I go to work, then i will get paid.
b. Your yard will not look good if you dont mow the grass

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