Question

Are the following statements true or false? Give reasons for your answers.
(1) Every whole number is a natural number
(2) Every integer is a rational number.
(3) Every rational number is an integer.


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Answer 1

Answer:

1. every whole number is not a natural number because whole numbers also includes 0 but on the other hand natural numbers do not include 0. Hence, every whole number is not a natural number.

2. Every integer is a rational number because every integer, including zero (0), fulfills the definition of a rational number.

3. No. Not every integer is a rational number, because integer means the collection of whole numbers and their negatives and it does not include numbers like 7/2 etc. But in the case of rational numbers, it has any number which can be represented in the form of p/q, where p and q are integers and q is not 0.

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Answer 2

Given :

• Are the following statements true or false? Give reasons for your answers.

　

(1) Every whole number is a natural number

(2) Every integer is a rational number.

(3) Every rational number is an integer.

Solution :

1. False.
2. True.
3. False.

Example and proofs :

• The number "zero" is a whole number whereas it's not a "natural number".

• Any integer can be expressed in the form of p/q form, hence this is called "rational number".

• The number which is in this form of p/q is not a "Integer".

Proof (1)

• "0" is not a natural number.

Proof (2)

• Integer "x" can be expressed in "p/q" form = (x/1).

Proof (3)

• The number in p/q form "1/5" is not an integer.