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Chapter 1: Q72. (page 17)

If aand bare natural numbers, then which of the following must also be a natural number?

I.a鈭�bII.abIII.abI.a-bII.abIII.ab

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

Short Answer

Expert verified

Correct option is (B) II only

Step by step solution

01

- Define natural number

The set 1,2,3,4,5,... is called the set of natural number.

02

- Substitution

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

I.1-2II.1脳2III.12

03

- Simplify three statements

To evaluate first statement, subtract 2 from 1

1-2=-1

To simplify second statement, multiply 1 with 2

1脳2=2

To evaluate third statement, divide 1 with 2

12=0.5

04

- Check given three statements are true or not

As -1and 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.

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