Q72. - Algebra 2

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

Step-by-Step Solution

Answer

Correct option is (B) II only

Step 1 - Define natural number

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

Step 2 - Substitution

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

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

Step 3 - 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

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

Step 4 - 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.