Proposition 1D
Given the following proposition:
∼ (A • ∼ X) ≡ [A ⊃ (Y ∨ ∼ B)]
-Given that A and B are true and X and Y are false, determine the truth value of Proposition 1D.

Question

Quizplus · Accepted Answer

Substituting the given truth values for A, B, X, and Y into the proposition:
∼ (A • ∼ X) ≡ [A ⊃ (Y ∨ ∼ B)]
∼ (T • ∼ F) ≡ [T ⊃ (F ∨ ∼ T)]
∼ (T • T) ≡ [T ⊃ T]
∼ T ≡ T
F ≡ T (by the rule of material implication)
This is a contradiction, so the proposition is always false. Therefore, the answer is B. However, since B is not an option, the closest answer is A (which would be the answer if the proposition were a tautology).

Proposition 1D Given the Following Proposition