Question

Determine the truth value of the following statement given \( p=T, q=T, r=F \) \[ (p \vee \sim r) \leftrightarrow(\sim q \rightarrow p) \]

Answer 1

To determine the truth value of the given statement, substitute the given values of p, q, and r and evaluate it. The statement ((p ∨ ¬r) ↔ (¬q → p)) is true.

Step-by-step explanation:

To determine the truth value of the statement, we substitute the given values of p, q, and r into the statement and evaluate it. We have p = T, q = T, and r = F.

1. For the left side of the statement, (p ∨ ¬r), we have (T ∨ ¬F), which simplifies to (T ∨ T), resulting in T.
2. For the right side of the statement, (q → p), we have (T → T), which simplifies to (F → T), resulting in T.

Finally, we compare the truth values of the left and right sides. Since both sides evaluate to T, the statement ((p ∨ ¬r) ↔ (¬q → p)) is true.