Question

9
2. Are the following statements true or false ?
Give reasons for your answers.
(i) Every whole number is a natural number.
(ii) Every whole number is a rational number.
(iii) Every integer is a rational number.
(iv) Every rational number is a whole number.

Answer 1

Answer:

False

True

True

False

Hope it's helpful

Answer 2

Answer:

(i)   False

(ii)  True

(iii) True

(iv) False

Reasons:

(i) Natural numbers (N)= Integers from 1 to infinity

  Whole numbers (W)= Integers from 0 to infinity

Hence, every natural number is a whole number, but, every whole number is not a natural number.

(ii) A rational number is any number that can be written (expressed) as a fraction. For example, 2.5 is a rational number because it can be expressed as 2

/5

.

​Whereas, a whole number is a positive number without a fraction or decimal.

Therefore, the opposite is true:

Every whole number is a rational number because it can be written as a fraction. 5 can be written as 1/5.

Remember that, every rational number is not a whole number.

(iii) Every integer is a rational number since each integer 'n' can be written in the form n/1. For example;

5 = 5/1 and thus 5 is a rational number.

However, numbers like:

1/2, 45454737/2424242, and -3/7 are also rational since they are fractions whose numerator and denominator are integers.

(iv) Please refer to the (ii) question's reasoning.

I hope you have found the answer you were looking for.

HAPPY LEARNING!