Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression.
-(Z $ \lor $ ∼A) ≡ [(A $ \lor $ ∼Z) ⊃ (X ≡ ∼X)]
A) True
B) False
C) Unknown

Question

Quizplus · Accepted Answer

Given A, B, C are true and X, Y, Z are false, we evaluate the expression step by step. Z $ \lor $ ∼A is false since Z is false and ∼A is false (because A is true). A $ \lor $ ∼Z is true since A is true regardless of Z's value. X ≡ ∼X is true because both X and its negation ∼X would be false, making their equivalence true. Therefore, the implication [(A $ \lor $ ∼Z) ⊃ (X ≡ ∼X)] is true because a true statement implies another true statement. Since both sides of the equivalence (≡) are true, the overall expression is true.

Assume A, B, C Are True; X, Y, Z Are ∨ \lor ∨

Assume A, B, C Are True; X, Y, Z Are $\lor$