JEE Main 2013 (Online) 23rd AprilQuestion 1
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
Sets, Relations and Function
Solution
If $m$ is prime and $m\mid n^2$, then by Euclid's lemma $m\mid n$, so $Q\wedge R\to P$ holds. The others fail: $m=4,n=2$ gives $Q$ true but $P,R$ false.