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

Question

Quizplus · Accepted Answer

[(A • ∼ X) ⊃ (∼ B ≡ Y)] • [∼ (Y ∨ ∼ A) ≡ (B • X)]

Substituting the given truth values:

[(T • ∼ F) ⊃ (∼ T ≡ F)] • [∼ (F ∨ ∼ T) ≡ (T • F)]

Simplifying:

[T ⊃ (F ≡ F)] • [∼(F ∨ T) ≡ F]

[T ⊃ T] • [∼T ≡ F]

T • F

Therefore, the proposition is false.

Proposition 2D Given the Following Proposition