Given two finite sets $A$ and $B$ such that $n(A) = 2, n(B) = 3$. Then total number of relations from $A$ to $B$ is

Let $R$ be a relation from $N$ to $N$ defined by $R =\left\{(a, b): a, b \in N \text { and } a=b^{2}\right\} .$ Are the following true?

$(a, b) \in R ,(b, c) \in R$ implies $(a, c) \in R$

The Fig shows a relation between the sets $P$ and $Q$. Write this relation 

in set - bulider form,

What is its domain and range ?

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

The relation $R$ defined on the set of natural numbers as $\{(a, b) : a$ differs from $b$ by $3\}$, is given by

Let $A=\{1,2,3,4,6\} .$ Let $R$ be the relation on $A$ defined by $\{ (a,b):a,b \in A,b$ is exactly divisible by $a\} $

Find the range of $R$