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

- A
${2^9}$

- B
$6$

- C
$8$

- D
None of these

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 $R$ be the relation on $Z$ defined by $R = \{ (a,b):a,b \in Z,a - b$ is an integer $\} $ Find the domain and range of $R .$

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

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 $R$ 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?

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