Relations Test ...

Consider the set $$A=(1, 2, 3)$$ and the R be the smallest equivalence relation on R then R is

The relation $$R=\left\{ \left( 1,1 \right) ,\left( 2,2 \right) ,\left( 3,3 \right)  \right\} $$ on the set $$\left\{ 1,2,3 \right\} $$ is

If $  A  $ is a finite set containing n distinct elements, then the number of relations on A is equal to

If R is an equivalence relation on a set A, then $$R^1$$ is 

Let  $$N$$  denotes the set of all natural numbers and  $$R$$  be the relation on  $$N \times N$$  defined by  $$( a , b ) R ( c , d )$$ iff  $$a d ( b + c ) = b c ( a + d ) ,$$  then  $$R$$  is

Let $$R:N \to N$$ be defined by $$R = \{ (a,b):a,b \in N$$ and $$a = {b^2}\}$$ then, which of the following is true? 

Let $$A$$ be set of first ten natural numbers and $$R$$ be a relation on $$A$$ defined by (x , y) $$\in$$ $$R$$ $$\Rightarrow$$ x + 2y = 10 , then domain of $$R$$ is

If $$h=\left\{ ((x,y),(x-y, x+y))/ x,y \epsilon  N \right\}  $$ is a relation on NxN, then domain of h

If $$A=\left\{ x:{ x }^{ 2 }-3x+2=0 \right\} $$, and R is a universal relation on A, then R is 

Let $$R_1, R_2$$ are relation defined on $$Z$$ such that $$aR_1b \Longleftrightarrow (a - b)$$ is divisible by $$3$$ and $$a \,R_2 b \Longleftrightarrow (a - b)$$ is divisible by $$4$$. Then which of the two relation $$(R_1 \cup R_2), (R_1 \cap R_2)$$ is an equivalence relation?