The relation $R$ defined on a set $A$ is antisymmetric if $(a,\,b) \in R \Rightarrow (b,\,a) \in R$ for

Let $R$ be a relation on $N \times N$ defined by $(a, b) R$ (c, d) if and only if $a d(b-c)=b c(a-d)$. Then $R$ is

Let $R$ be a relation on $Z \times Z$ defined by$ (a, b)$$R(c, d)$ if and only if $ad - bc$ is divisible by $5$ . Then $\mathrm{R}$ is

Let $R$ be a relation on a set $A$ such that $R = {R^{ - 1}}$, then $R$ is

Let $R$ and $S$ be two relations on a set $A$. Then

Let $R = \{(1, 3), (2, 2), (3, 2)\}$ and $S = \{(2, 1), (3, 2), (2, 3)\}$ be two relations on set $A = \{1, 2, 3\}$. Then $RoS =$