Question

Statement-1 : ~ (p ↔ ~q) is equivalent to p ↔ q.
Statement-2 : ~ (p ↔ ~q) is a tautology.

(a) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
(b) Statement- 1 is true, Statement-2 is false
(c) Statement-1 is false, Statement-2 is true
(d) Statement-1 is true, Statement-2 is true; Statement-2 is correct explanation for Statement-1

Answer 1

(b) : Let’s prepare the truth table

As the column for ~(p ↔ ~q) and (p ↔ q) is the same, we conclude that ~(p ↔ ~q) is equivalent to (p ↔ q). 

~(p ↔ ~q) is NOT a tautology because it’s statement value is not always true.