# S1:$^{\sim} (p \leftrightarrow\: ^{\sim} q)$ is equivalent to $p \leftrightarrow q.$  S2 :$^{\sim} (p\leftrightarrow \: ^{\sim} q)$ is a tautology.

$\begin {array} {1 1} \text{(A) S1 is true, S2 is true,S2 is a correct explanation for S1} \\ \text{(B) S1 is true, S2 is true, S2 is not a correct explanation for S1} \\ \text{(C) S1 is true, S2 is false} \\ \text{(D) S1 is false, S2 is true} \end {array}$

 p q $p \leftrightarrow q$ $^{\sim}q$ $p \leftrightarrow \: ^{\sim}q$ $^{\sim} (p \leftrightarrow \: ^{\sim}q)$ T T T F F T T F F T T F F T F F T F F F T T F T
Ans : (C)

edited Jan 22, 2014