# Trouble determining truth value of logic statements

• MHB
• chelseajjc95
In summary, the first statement evaluates to $F$ and the second statement's truth value depends on the truth value of $r$.
chelseajjc95
For the folowing two problems determine the truth value of each statement:
assume a and b are true and c and d are false.

not(a V b) -> s
not( T V T) -> s
F -> s
T

r -> [(d -> w) <-> (a ^ c )]
r -> [(F -> w) <-> ( T ^ F)]
r -> [T <-> F]
r -> F

I am fairly certain I did the first one correct but I would like some confirmation. The second one I am unsure how to evaluate
because the value of r is unknown and if r is t then the statement will be false but if r is false then the statement will be true.

You are right: $r\to [(d\to w) \leftrightarrow (a\land c )]$ is equivalent to $\neg r$ under the assumptions about $a$, $b$, $c$ and $d$, so the original formula does not have a definite truth value.

## 1. What is the definition of "truth value" in logic?

Truth value in logic refers to the validity or accuracy of a statement, based on whether it is true or false.

## 2. How do you determine the truth value of a logic statement?

The truth value of a logic statement can be determined by examining its logical form and comparing it to established rules of logic, such as the law of non-contradiction.

## 3. What are the common challenges in determining the truth value of logic statements?

Some common challenges in determining the truth value of logic statements include unclear or ambiguous language, faulty logic, and incomplete information.

## 4. Can a logic statement have a truth value of both true and false?

No, a logic statement cannot have a truth value of both true and false. It can only have one truth value, either true or false, based on its logical form and the evidence or information available.

## 5. How does determining the truth value of logic statements relate to the scientific method?

The process of determining the truth value of logic statements is similar to the scientific method, as it involves observation, evidence, reasoning, and testing. Both use logical reasoning to determine the validity or accuracy of a statement or claim.

• Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
24
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
8
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
9
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
17
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
18
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
6
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
8
Views
2K