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) ${x : x = 3 n - 2, n \in W, n \leq 8}$ (v) ${x : x = 3 n - 2, n \in Z, n \leq 8}$ (vi) ${x : x = \frac{n - 2}{n + 1}, n \in W}$

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Solution

(i) The set of multiples of 8 = ${8, 16, 24, 32, . . . . . .} It is an infinite set$ (ii) The set of integers less than 10 = ${9, 8, 7, 6, 5, 4, 3, 2, 1, - 1, - 2, . . . . . .} It is an infinite set$ (iii) The set of whole numbers less than 12 = ${11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, . . . . . .} It is a finite set$ (iv) ${x : x = 3 n - 2, n \in W, n \leq 8}$ Substituting the value of n = (0,1,2,3,4,5,6,7 and 8) we get = ${- 2, 1, 4, 7, 10, 13, 16, 19, 22......} It is an finite set$ (v) ${x : x = 3 n - 2, n \in Z, n \leq 8} = {22, 19, 16, 13, 10, 7, 4, 1, - 2, - 5......} It is a infinite set$ (vi) ${x : x = \frac{n - 2}{n + 1}, n \in W}$ ${- 2, - \frac{1}{2}, 0 \frac{1}{4}, \frac{2}{5} . . . . . .} It is infinite set$

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