Statement $-1$ : $ \sim \left( {p \leftrightarrow \, \sim q} \right)$ is equivalent to $p \leftrightarrow q$
Statement $-2$ : $ \sim \left( {p \leftrightarrow \, \sim q} \right)$ is a tautology.
Statement $-1$ is True, Statement $-2$ is True;
Statement $-2$ is a correct explanation for Statement $-1$ .
Statement $-1$ is True, Statement $-2$ is True;
Statement $-2$ is $NOT$ a correct explanation for Statement $-1$ .
Statement $-1$ is True, Statement $-2$ is False.
Statement $-1$ is False, Statement $-2$ is True.
The negation of the statement $''96$ is divisible by $2$ and $3''$ is
The Boolean Expression $\left( {p\;\wedge \sim q} \right)\;\;\vee \;q\;\;\vee \left( { \sim p\wedge q} \right)$ is equivalent to:
The statement $(p \wedge(\sim q) \vee((\sim p) \wedge q) \vee((\sim p) \wedge(\sim q))$ is equivalent to
For the statements $p$ and $q$, consider the following compound statements :
$(a)$ $(\sim q \wedge( p \rightarrow q )) \rightarrow \sim p$
$(b)$ $((p \vee q) \wedge \sim p) \rightarrow q$
Then which of the following statements is correct?