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

roster form

What is its domain and range?

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

$(a, a) \in R$ for all $a \in Q$

Define a relation $R$ on the set $N$ of natural numbers by $R=\{(x, y): y=x+5$ $x $ is a natural number less than $4 ; x, y \in N \} .$ Depict this relationship using roster form. Write down the domain and the range.

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

Write down the domain, codomain and range of $R .$

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