Let $A = \{1, 2, 3\}$. The total number of distinct relations that can be defined over $A$ is

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 $R .$

Let $A=\{1,2,3, \ldots, 14\} .$ Define a relation $R$ from $A$ to $A$ by $R = \{ (x,y):3x - y = 0,$ where $x,y \in A\} .$ Write down its domain, codomain and range.

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 $A=\{x, y, z\}$ and $B=\{1,2\} .$ Find the number of relations from $A$ to $B$.

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