Q. 44.1( 434 Votes )

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.

Answer :

(i) True, since the collection of whole numbers contains all natural numbers.

Natural numbers are numbers starting from 1, i.e 1, 2, 3, 4, 5, 6, ..................
And whole numbers are numbers starting from 0. i.e, 0, 1, 2, 3, 4, 5.............

And you can see that all natural numbers are within whole numbers.

(ii) False, as integers may be negative or positive but whole numbers are always positive.

Now integers are numbers that are both negative and positive and include zero also, i.e, ..........-3, -2, -1, 0, 1, 2, 3, 4, .......
And whole numbers are numbers starting from 0. i.e, 0, 1, 2, 3, 4, 5............

And clearly, negative numbers are missing from whole numbers.

(iii) False, as rational numbers may be fractional but whole numbers are not fractional.

Now, Rational numbers are numbers that can be expressed in p/q form where q not equal to zero. So they include fractions on the other hand whole numbers are numbers starting from 0. i.e, 0, 1, 2, 3, 4, 5............

Therefore, Whole numbers does  not contain all rational numbers.

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