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

Question

Quizplus · Accepted Answer

Given A=true, B=true, X=false, Y=false, the left side of the main conditional [(X ⊃ ∼Y) • ∼(X ∨ ∼B)] simplifies to true because (X ⊃ ∼Y) is true (since false implies anything is true) and ∼(X ∨ ∼B) is true (since X is false and B is true, making ∼B false and X ∨ ∼B false, thus its negation true). The right side [∼(B ⊃ ∼Y) ≡ (A • ∼Y)] simplifies to false ≡ false, which is true (since B ⊃ ∼Y is false implies true, which is true, making its negation false; A • ∼Y is true and true, which simplifies to false because Y is false). Therefore, the entire proposition simplifies to true ⊃ true, which is true, contradicting the initial determination.

Proposition 2F Given the Following Proposition