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
$Q \wedge R \to P$
$P \wedge Q \to R$
$Q \to R$
$Q \to P$
The proposition $p \rightarrow \sim( p \wedge \sim q )$ is equivalent to
The negation of the compound proposition $p \vee (\sim p \vee q)$ is
$p \Rightarrow q$ can also be written as
If statement $(p \rightarrow q) \rightarrow (q \rightarrow r)$ is false, then truth values of statements $p,q,r$ respectively, can be-
If $P$ and $Q$ are two statements, then which of the following compound statement is a tautology?