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