devarshi-dt-logo

Question:

Statement 1: ¬(p↔¬q) is equivalent to p↔q
Statement 2: ¬(p↔¬q) is a tautology
Choose the correct option:
Both Statement 1 and Statement 2 are true and Statement 2 is a correct explanation for statement 1
Both Statement 1 and Statement 2 are true and Statement 2 is not a correct explanation for Statement 1
Statement 1 is false but Statement 2 is true
Statement 1 is true but statement 2 is false

Statement 1 is true but statement 2 is false

Both Statement 1and Statement 2 are true and Statement 2 is not a correct explanation for Statement 1

Both Statement 1 and Statement 2 are true and Statement 2 is a correct explanation for statement 1

Statement 1 is false but Statement 2 is true

Solution:

p q ¬p ¬q p↔¬q ¬(p↔¬q) p↔q
T T F F F T T
T F F T T F F
F T T F F T F
F F T T T F T
Clearly, ¬(p↔¬q) is not a tautology because it does not contain T in the column of its truth table. Also, ¬(p↔¬q) and p↔q have the same truth value
Hence, option 'A' is correct.