Relations Test ...

A relation $$R$$ is defined on the set $$Z$$ of integers as follows: R=$$(x,y)$$ $$\displaystyle \in {R}:x^{2}+y^{2}= 25$$. Express $$R$$ and $$\displaystyle R^{-1}$$ as the sets of ordered pairs and hence find their respective domains.

If $$A=\left\{ 2,3 \right\} $$ and $$B=\left\{ 1,2,3,4 \right\} $$, then which of the following is not a subset of $$A\times B$$

In order that a relation $$R$$ defined in a non-empty set $$A$$ is an equivalence relation, it is sufficient that $$R$$

Which one of the following relations on $$R$$ is equivalence redlation-

$$A$$ and $$B$$ are two sets having $$3$$ and $$4$$ elements respectively and having $$2$$ elements in common. The number of relations which can be defined from $$A$$ to $$B$$ is

If $$A=\left\{ 2,4,5 \right\} , B=\left\{ 7,8,9 \right\} $$ then $$n(A\times B)$$ is equal to-

Let $$X=\left\{ 1,2,3,4 \right\} $$ and $$Y=\left\{ 1,2,3,4 \right\} $$. Which of the following is a relation from $$X$$ to $$Y$$.

If $$A=\left\{ 1,2,3 \right\} , B=\left\{ 1,4,6,9 \right\} $$ and $$R$$ is a relation from $$A$$ to $$B$$ defined by '$$x$$ is greater than $$y$$'. Then range of $$R$$ is

Let $$g\left( x \right)=1+x-\left[ x \right] $$ and $$f\left( x \right)=\begin{cases} \begin{matrix} -1 & x<0 \end{matrix} \\ \begin{matrix} 0 & x=0 \end{matrix} \\ \begin{matrix} 1 & x>0 \end{matrix} \end{cases}$$. Then for all $$x,f\left[ g\left( x \right) \right] $$ is equal to

If $$A = \left\{1,2,3\right\}$$, $$B = \left\{1,4,6,9\right\}$$ and $$R$$ is relation from $$A$$ to $$B$$ defined by $$'x'$$ is greater than $$'y'$$. Then range of $$R$$ is