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

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

For real numbers $x$ and $y$, we write $ xRy \in $ $x - y + \sqrt 2 $ is an irrational number. Then the relation $R$ is

Let $N$ denote the set of all natural numbers and $R$ be the relation on $N \times N$ defined by $(a, b)$ $R$ $(c, d)$ if $ad(b + c) = bc(a + d),$ then $R$ is

Let $N$ be the set of natural numbers and a relation $R$ on $N$ be defined by $R=\left\{(x, y) \in N \times N: x^{3}-3 x^{2} y-x y^{2}+3 y^{3}=0\right\} .$ Then the relation $R$ is:

Let $X$ be a family of sets and $R$ be a relation on $X$ defined by $‘A$ is disjoint from $B’$. Then $R$ is