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

Question

Quizplus · Accepted Answer

Starting with the first part of the proposition: 
∼[(A ≡ ∼ Y) • (B ⊃ X)] 
We substitute in the given truth values: 
∼[(true ≡ true) • (true ⊃ false)] 
Simplifying, we get: 
∼[true • false] 
Which is equivalent to: 
∼false 
Therefore, the first part of the proposition is true. 
Moving on to the second part: 
[(B ∨ ∼ X) • (X ≡ A)] 
Again, substituting in the given truth values: 
[(true ∨ true) • (false ≡ true)] 
Simplifying, we get: 
[true • false] 
Which is equivalent to: 
false 
Therefore, the second part of the proposition is false. 
Combining the two parts using the conjunction "•", we get: 
true • false 
Which is equivalent to: 
false 
Therefore, the entire proposition is false.

Proposition 2C Given the Following Proposition