The statement $p \rightarrow (q \rightarrow p)$ is equivalent to
$p \rightarrow (p \rightarrow q)$
$p \rightarrow (q\, \vee \, p)$
$p \rightarrow (q\, \wedge p)$
$p \rightarrow (p \leftrightarrow q)$
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 is always true
The statement "If $3^2 = 10$ then $I$ get second prize" is logically equivalent to
The inverse of the proposition $(p\; \wedge \sim q) \Rightarrow r$ is
The false statement in the following is