The inverse of the proposition $(p\; \wedge \sim q) \Rightarrow r$ is

Which of the following is a contradiction

$\sim (p \vee q) \vee (~ p \wedge q)$ is logically equivalent to

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

The negation of the expression $q \vee((\sim q) \wedge p)$ is equivalent to

Consider

Statement $-1 :$$\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \wedge q} \right)$ is a fallacy.

Statement $-2 :$$(p \rightarrow q) \leftrightarrow ( \sim q \rightarrow   \sim  p )$  is a tautology.