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

Question

Quizplus · Accepted Answer

Using the truth values for A, B, X, and Y given in the question, we can simplify the proposition as follows:

- (A ⊃ Y) ≡ (B ⊃ ∼X) is true, since the antecedents of both conditionals are true and the consequents match in their truth values.
- (B • ∼X) ≡ (Y • A) is false, since the left side evaluates to false (since B is true and X is false), while the right side evaluates to true (since Y is false and A is true). Therefore, its negation, ∼[(B • ∼X) ≡ (Y • A)], is true.

Thus, we have:
[(A ⊃ Y) ≡ (B ⊃ ∼X)] ∨ ∼[(B • ∼ X) ≡ (Y • A)]
= (true ≡ true) ∨ true
= true ∨ true
= true

Therefore, Proposition 2B is true.

Proposition 2B Given the Following Proposition