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

Consider the following statements:

$P :$ Ramu is intelligent

$Q $: Ramu is rich

$R:$ Ramu is not honest

The negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as.

The negative of the statement $\sim p \wedge(p \vee q)$ is

Let the operations $*, \odot \in\{\wedge, \vee\}$. If $( p * q ) \odot( p \odot \sim q )$ is a tautology, then the ordered pair $(*, \odot)$ is.

Which Venn diagram represent the truth of the statement“All students are hard working.”

Where $U$ = Universal set of human being, $S$ = Set of all students, $H$ = Set of all hard workers.