Question

If $a$and $b$are natural numbers, then which of the following must also be a natural number?

$\text{I.}a-b\text{II.}ab\text{III.}\frac{a}{b}$$\text{I.}a-b\text{II.}ab\text{III.}\frac{a}{b}$

(A) I only (B) II only (C) III only (D) I and II only (E) II and III only

Short answer

Correct option is (B) II only

Step-by-step solution

- Define natural number

The set $\left\{1,2,3,4,5,...\right\}$ is called the set of natural number.

- Substitution

Substitute 1 for a and 2 for b in given three statement

$\text{I.}1-2\text{II.}1\times 2\text{III.}\frac{1}{2}$

- Simplify three statements

To evaluate first statement, subtract 2 from 1

$1-2=-1$

To simplify second statement, multiply 1 with 2

$1\times 2=2$

To evaluate third statement, divide 1 with 2

$\frac{1}{2}=0.5$

- Check given three statements are true or not

As $-1$and 0.5 are not natural numbers, so statement I and III are not a natural number always.

Also product of two natural number is a natural number.

Thus, only statement II is true.

Thus option (B) is correct.