Question

If $A$ is the set of even natural numbers less than $8$ and $B$ is the set of prime numbers less than $7$, then the number of relations from $A$ to $B$ is

• A. $2^9$
• B. $9^2$
• C. $3^2$
• D. $2^9-1$

Answer 1

The correct option is A

$2^9$

Explanation for the correct option:

Find the number of relations from $A$ to $B$:

Given,

$A$ is the set of even natural numbers less than $8$,

$A=\left\{2,4,6\right\}$

$B$ is the set of prime numbers less than $7$,

$B=\left\{2,3,5\right\}$

As we know,

Number of relations $=2^{mn}$

Here, $m=3,n=3$

$\therefore$The number of relations from $A$ to $B$ $\mathbf{=}\mathbf{}{\mathbf{2}}^{\mathbf{9}}$

Hence, Option ‘A’ is Correct.