State whether each of the following sets is a finite set or an infinite set :

(i) The set of multiples of 8.

(ii) The set of integers less than 10.

(iii) The set of whole numbers less than 12.

(iv) {x : x = 3n - 2, n ∈ W, n ≤ 8}

(v) {x : x = 3n - 2, n ∈ Z, n ≤ 8}

(vi) ${\Big{x : x = \dfrac{n - 2}{n + 1}, n ∈ W\Big}}$

(i) Infinite

Reason

There are infinite multiple of 8.

A = {8, 16, 24, 32,……………}

(ii) Infinite

Reason

Integers less than 10 includes all negative numbers, 0 and positive number till 9.

B = {……………, -4, -3, -2, -1, 0 , 1, 2, 3, 4, 5, 6, 7, 8, 9}

(iii) Finite

Reason

Whole numbers less than 12 include all the numbers between 0 to 11

C = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

(iv) Finite

Reason

x = 3n - 2

When n = 0

x = 3 x 0 - 2 = 0 - 2 = -2

When n = 1

x = 3 x 1 - 2 = 3 - 2 = 1

When n = 2

x = 3 x 2 - 2 = 6 - 2 = 4

When n = 3

x = 3 x 3 - 2 = 9 - 2 = 7

When n = 4

x = 3 x 4 - 2 = 12 - 2 = 10

When n = 5

x = 3 x 5 - 2 = 15 - 2 = 13

When n = 6

x = 3 x 6 - 2 = 18 - 2 = 16

When n = 7

x = 3 x 7 - 2 = 21 - 2 = 19

When n = 8

x = 3 x 8 - 2 = 24 - 2 = 22

D = {-2, 1, 4, 7, 10, 13, 16, 19, 22}

(v) Infinite

Reason

Integers less than equal to 8 include all negative numbers, 0 and positive numbers till 8.

D = {……………, -8, -5, -2, 1, 4, 7, 10}

(vi) Infinite

Reason

${\Big{x : x = \dfrac{n - 2}{n + 1}, n ∈ W\Big}}$

When n = 0

x = $\dfrac{0 - 2}{0 + 1} = \dfrac{-2}{1} = -1$

When n = 1

x = $\dfrac{1 - 2}{1 + 1} = \dfrac{-1}{2}$

When n = 2

x = $\dfrac{2 - 2}{2 + 1} = \dfrac{0}{3} = 0$

When n = 3

x = $\dfrac{3 - 2}{3 + 1} = \dfrac{1}{4}$

Similarly n = 4, 5, 6, ……………. and hence we get the value of x for every value of n.