Relations Test ...

If $\displaystyle :n(A)= m,$ then number of relations in $A$ are

In order that a relation $R$ defined on a non-empty set $A$ is an equivalence relation.
It is sufficient, if $R$

Let $A= \{ 1,2,3,.......50\}$ and $B=\{2,4,6.......100\}$ .The number of elements $\left ( x, y \right )\in A\times B$ such that $x+y=50$

Let $\displaystyle A=  \left \{ a,b,c \right \}$ and $\displaystyle B=  \left \{ 4,5 \right \}$ Consider a relation $R$ defined from set $A$ to set $B$ then $R$ is subset of

If $A=\{2, 4\}$ and $B=\{3, 4, 5\}$ then $(A\cap B)\times (A\cup B)$ is

If $R$ is an anti symmetric relation in $\displaystyle A$ such that $(a,b),(b,a)\:\in\: R$ then

$R$ is a relation from $\displaystyle \left \{ 11,12,13 \right \}$ to $\displaystyle \left \{ 8,10,12 \right \}$ defined by $y=x-3$ then the $R^{-1}$ .

Let $A$ and $B$ be two finite sets having $m$ and $n$ elements respectively. Then the total number of mapping from $A$ to $B$ is

If $\displaystyle A=\left \{ 0,1,2,3,4,5 \right \}$ and relation $R$ defined by $a R b$ such that $2a+b=10$ then $R^{-1}$ equals

If $\displaystyle R=\{ (x,y):x, y \in Z ,x^{2}+y^{2}\leq 4 \}$ is a relation in $Z$ then domain $D$ is