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

Question

Quizplus · Accepted Answer

Breaking down the proposition with the given values: A = true, B = true, X = false, Y = false. The innermost expressions evaluate as follows: ∼(X ∨ ∼Y) simplifies to ∼(false ∨ true) = ∼true = false. (∼X ⊃ ∼A) simplifies to (true ⊃ false) = false. So, the equivalence part [∼(false) ≡ false] simplifies to true ≡ false, which is false. The right side of the disjunction, ∼(B • ∼A), simplifies to ∼(true • false) = ∼false = true. Therefore, the whole expression simplifies to false ∨ true, which is true. My initial evaluation was incorrect; the correct truth value of Proposition 1F, given the values of A, B, X, and Y, is true.

Proposition 1F Given the Following Proposition