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

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

in set-builder form 

What is its domain and range?

Let $A=\{1,2\}$ and $B=\{3,4\} .$ Find the number of relations from $A$ to $B .$

Let $R$ be a relation from $Q$ to $Q$ defined by $R=\{(a, b): a, b \in Q$ and $a-b \in Z \} .$ Show that

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

Let $A=\{1,2,3,4,5,6\} .$ Define a relation $R$ from $A$ to $A$ by $R=\{(x, y): y=x+1\}$

Depict this relation using an arrow diagram.

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 $(a, c) \in R$