Answer to Question #316600 in Discrete Mathematics for denz

Question

1. Show, by the use of the truth table/matrix, that the statement 

(P ⇒ Q) ⇔ (!Q ⇒ !P) is a tautology.

1. Show that P ⇔ Q ≡ (P ^ Q) v (!P ^ !Q) are logically equivalent.

Answer 1

As we can see, far right column contains only 1, which means the proposition is a tautology

I will show it using the truth table

As we can see, two last columns are equal, which means this propositions are logically equivalent