Solution set of $x \equiv 3$ (mod $7$), $p \in Z,$ is given by

Let $R$ be a relation defined on $N \times N$ by $(a, b) R(c, d) \Leftrightarrow  a(b + c) = c(a + d).$ Then $R$ is

The relation $R =\{( a , b ): \operatorname{gcd}( a , b )=1,2 a \neq b , a , b \in Z \}$ is:

Let $S$ be set of all real numbers ; then on set $S$ relation $R$ defined as $R = \{\ (a, b) : 1 + ab > 0\ \}$ is

Let $R_{1}$ and $R_{2}$ be relations on the set $\{1,2, \ldots, 50\}$ such that $R _{1}=\left\{\left( p , p ^{ n }\right)\right.$ : $p$ is a prime and $n \geq 0$ is an integer $\}$ and $R _{2}=\left\{\left( p , p ^{ n }\right)\right.$ : $p$ is a prime and $n =0$ or $1\}$. Then, the number of elements in $R _{1}- R _{2}$ is........

If $R$ is a relation from a finite set $A$ having $m$ elements to a finite set $B$ having $n$ elements, then the number of relations from $A$ to $B$ is