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

Question

Quizplus · Accepted Answer

Breaking down the proposition with the given values: A=true, B=true, X=false, Y=false. The first part ∼[(A ⊃ Y) ∨ ∼(X ⊃ B)] simplifies to ∼[false ∨ true] = ∼true = false, because (A ⊃ Y) is false when A is true and Y is false, and ∼(X ⊃ B) is false when X is false and B is true, making the whole expression true, which is then negated to false. The second part [∼(A ≡ ∼X) ∨ (B ⊃ X)] simplifies to [true ∨ false] = true, because ∼(A ≡ ∼X) is true when A is true and X is false (since A ≠ ∼X), and (B ⊃ X) is false when B is true and X is false. Combining both parts with the conjunction operator (•) results in false • true, which is false.

Proposition 2G Given the Following Proposition