Relations Test ...

 from the given statement $$N$$ denotes the natural number and $$W$$ denotes the whole number, so which statement in the following is correct

Which one of the following relations on $$R$$ is equivalence relation

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

If $$A = \left\{2,3\right\}$$ and $$B = \left\{1,2\right\}$$, then $$A \times B$$ is equal to 

$$A$$ 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

Let $$X = \left\{1,2,3,4\right\}$$ and $$Y = \left\{1,3,5,7,9\right\}$$. Which of the following is relations from $$X$$ to $$Y$$

If $$R$$ is a relation from a finite set $$A$$ having $$m$$ elements to a finite set $$B$$ having $$n$$ elements, then the number of relations from $$A$$ to $$B$$ is:

The relation $$R$$ is defined in $$A = \left\{1,2,3\right\}$$ by $$a\ R$$ $$b$$ if $$|a^2 - b^2| \le 5$$. Which of the following is false?

If $$R = \{(x, y):3x + 2y = 15 \text{ and }x\,, y\,\in \, N\}$$, the range of the relation R is .........

Let $$n(A) = n$$. Then the number of all relations on $$A$$ is