Q. 53.8( 37 Votes )

# Are the following statements true or false? Give reasons for your answer.

(i) Every whole number is a natural number.

(ii) Every integer is a rational number.

(iii) Every rational number is an integer.

(iv) Every natural number is a whole number.

(v) Every integer is a whole number.

(vi) Every rational number is a whole number

Answer :

(i) False: As whole numbers include zero, whereas natural numbers doesn’t include zero.

(ii) True: As integers are a part of rational numbers.

(iii) False: As integers are a part of natural numbers.

(iv) True: As whole numbers include all the natural numbers.

(v) False: As whole numbers are a part of integers.

(vi) False: As rational numbers include all the whole numbers.

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State whether the following statements are true or false? Justify your answer.

is written in the form 𝑝𝑞, 𝑞 ≠0 and so it is a rational number.

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There are infinitely many integers between any two integers.

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is not a rational number as √12 and √3 are not integers.

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RS Aggarwal & V Aggarwal - Mathematics