State whether the following statements are true or false. Give reasons for your answers
(i) Every natural number is a whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number.

Solution:

(i) Every natural number is a whole number.

This statement is true because the set of natural numbers is represented as N = {1, 2, 3...} and the set of whole numbers is W = {0, 1, 2, 3...}. We see that every natural number is present in the set of whole numbers. For example, 5 is a natural number as well as a whole number.

ii) Every integer is a whole number.

This statement is false because the set of integers is represented as Z = { -2, -1, 0, 1, 2...} and the set of whole numbers is W = {0, 1, 2, 3...}. We see that the negative integers are not the elements of the whole numbers set. Thus, negative integers are not a subset of whole numbers. For example, -2 is an integer but not a whole number.

iii) Every rational number is a whole number.

This statement is false as every number represented in the form of p/q where q ≠ 0 does not get simplified to a whole number. For example, 1/2 is a rational number, but not a whole number.

Video Solution:

State whether the following statements are true or false. Give reasons for your answers (i) Every natural number is a whole number. (ii) Every integer is a whole number. (iii) Every rational number is a whole number.

NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.1 Question 4:

Summary:

The statement "Every natural number is a whole number" is true, the statements "Every integer is a whole number" and "Every rational number is a whole number" are false.

☛ Related Questions:

• Is zero a rational number? Can you write it in the form p/q, where p and q are integers and q ≠ 0?
• Find six rational numbers between 3 and 4.
• Find five rational numbers between 3/5 and 4/5.