Question

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

Answer 1

Answer:

1 true, all natural no. are whole no.

2 false, every whole no. are integers but every integers are not whole no.

3 false, every whole no. are rational no. but it is not necessary that every rational no. are not whole no.

Step-by-step explanation:

This is the correct answer....❤️

Answer 2

(i) True

Natural numbers- Numbers starting from 1 to infinity (without fractions or decimals)i.e., Natural numbers= 1,2,3,4…

Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals)i.e., Whole numbers= 0,1,2,3…

Or, we can say that whole numbers have all the elements of natural numbers and zero.

Every natural number is a whole number; however, every whole number is not a natural number.

(ii) False

Integers- Integers are set of numbers that contain positive, negative and 0; excluding fractional and decimal numbers. i.e., integers={…-4,-3,-2,-1,0,1,2,3,4…}

Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals)

i.e., Whole numbers= 0,1,2,3….

Hence, we can say that integers include whole numbers as well as negative numbers.

Every whole number is an integer; however, every integer is not a whole number.

(iii) False

Rational numbers- All numbers in the form p/q, where p and q are integers and q≠0. i.e., Rational numbers = 0, 19/30 , 2, 9/-3, -12/7…

Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals) i.e., Whole numbers= 0,1,2,3….

Hence, we can say that integers includes whole numbers as well as negative numbers.

Every whole numbers are rational, however, every rational numbers are not whole numbers.