Relations Test ...

Let $$R$$ be the relation on $$Z$$ defined by $$R = \{(a, b): a, b \in z, a - b$$ is an integer$$\}$$. Find the domain and Range of $$R$$.

Find x and y, if $$(x+3,5)=(6,2x+y)$$.

A relation $$R$$ is defined from $$\left\{ 2,3,4,5 \right\} $$ to $$\left\{ 3,6,7,10 \right\} $$ by:

The relation $$R$$ in $$N\times N$$ such that $$(a,b)R(c,d)\Leftrightarrow a+d=b+c$$ is

Let $$R$$ be the relation over the set of all straight lines in a plane such that $${l}_{1}$$ $$R$$ $${l}_{2}\Leftrightarrow {l}_{1}\bot {l}_{2}$$. Then, $$R$$ is

Let $$R$$ be a relation on the set $$N$$ given by $$R=\left\{ \left( a,b \right) :a=b-2,b>6 \right\}$$. Then

If $$A=\left\{ a,b,c \right\} $$, then the relation $$R=\left\{ \left( b,c \right)  \right\} $$ on $$A$$ is

Which of the following is not an equivalence relation on $$Z$$?

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 $$y$$. The range of $$R$$ is

A relation $$\phi$$ from $$C$$ to $$R$$ is defined by $$x\phi y\Leftrightarrow \left| x \right| =y$$. Which one is correct?