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

Question

Quizplus · Accepted Answer

Breaking down the proposition with the given values: A = true, B = true, X = false, Y = false. 1. $B \equiv \sim Y$ becomes $true \equiv true$ because $B$ is true and $\sim Y$ (not Y) is also true since $Y$ is false. This part evaluates to true.2. $\sim(\sim X \supset A)$ becomes $\sim(false \supset true)$. Since $\sim X$ is true (because $X$ is false), and $A$ is true, $false \supset true$ is true, making $\sim(true)$ false.3. $\sim(X \equiv A)$ becomes $\sim(false \equiv true)$, which is $\sim false$ or true.4. $Y \cdot \sim A$ becomes $false \cdot false$ which is false.So, the proposition simplifies to $[true \cdot false] \lor [true \supset false]$. The left side of the disjunction $\lor$ is false, and the right side, $true \supset false$, is false because a true proposition cannot imply a false one. Thus, the entire proposition is false.

Proposition 1I Given the Following Proposition