Proposition 2E
Given the following proposition:
[∼ (A ∨ Y) ≡ (∼ X ⊃ B)] ∨ [∼ (Y • ∼ B) ⊃ (X ⊃ ∼ A)]
-Given that A and B are true and X and Y are false, determine the truth value of Proposition 2E.

Question

Quizplus · Accepted Answer

Plugging in the given truth values, we have:
[∼(T ∨ F) ≡ (∼ F ⊃ T)] ∨ [∼(F • ∼ T) ⊃ (F ⊃ ∼ T)]
Simplifying, we get:
[∼T ≡ T] ∨ [T ⊃ T]
Which is equivalent to:
F ∨ T
And since F ∨ anything always evaluates to True, Proposition 2E is true.

Proposition 2E Given the Following Proposition