If the truth value of the statement $p \to \left( { \sim q \vee r} \right)$ is false $(F)$, then the truth values of the statement $p, q, r$ are respectively
$T, T, F$
$F, T, T$
$T, F, T$
$T, F, F$
For integers $m$ and $n$, both greater than $1$ , consider the following three statements
$P$ : $m$ divides $n$
$Q$ : $m$ divides $n^2$
$R$ : $m$ is prime,
then true statement is
Which of the following pairs are not logically equivalent ?
If the Boolean expression $\left( {p \oplus q} \right) \wedge \left( { \sim p\,\Theta\, q} \right)$ is equivalent to $p \wedge q$, where $ \oplus $ , $\Theta \in \left\{ { \wedge , \vee } \right\}$ , ,then the ordered pair $\left( { \oplus ,\Theta } \right)$ is
The contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is
If $(p\; \wedge \sim r) \Rightarrow (q \vee r)$ is false and $q$ and $r$ are both false, then $p$ is