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

Question

Quizplus · Accepted Answer

Substituting the given values in the proposition, we get:
[∼(false ∨ true) ≡ (∼ false ⊃ ∼ false)] ≡ ∼[(true ⊃ ∼ false) • ∼(∼ false ⊃ ∼ true)]
Simplifying further:
[∼ true ≡ true] ≡ ∼[(true ⊃ true) • ∼(true ⊃ false)]
[false ≡ true] ≡ ∼[(true) • false]
false ≡ ∼false
true
Therefore, Proposition 2I is true.

Proposition 2I Given the Following Proposition