Relations Test ...

Let $$R$$ be a reflexive relation on a finite set $$A$$ having $$n$$ elements, and let there be $$m$$ ordered pairs in $$R,$$ then:

Total number of equivalence relations defined in the set $$S =\{a,b,c\}$$ is

If relation $$R$$ is defined by $$\mathrm{R}=\{(\mathrm{x},\ \mathrm{y}):2\mathrm{x}^{2}+3\mathrm{y}^{2}\leq 6\}$$, then the domain of $$\mathrm{R}$$ is

The domain and range of relation $$R=\{(x,y) | x, y \in N$$, $$x+2y=5\} $$ is?

Let $$A$$ be a non-empty set such that $$A \times A$$ has $$9 $$ elements among which are found $$(-1, 0)$$ and $$(0, 1)$$, then

Given the relation $$R =\{(1,2) (2,3)\}$$ on the set $$A=\{1,2,3\}$$, the minimum number of ordered pairs which when added to $$R$$ to make it an equivalence relation is

Which one of the following relations on Z is equivalence relation?

Which of the following are not equivalence relations on $$I$$?

The number of relations from $$ A=\left \{ 1,2,3 \right \} $$ to $$B = \left \{ 4,6,8,10 \right \}$$ is

The range of the function $$f(x)=\dfrac{\sin(\pi [x])}{x^{2}+1}$$ (where $$[.]$$ denotes greatest integer function) is