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Question

Write the following sets in the set-builder form:

(i) {3, 6, 9, 12} (ii) {2, 4, 8, 16, 32}

(iii) {5, 25, 125, 625} (iv) {2, 4, 6,........}

(v) {1, 4, 9,........,100}

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Solution

(i) Let A = {3, 6, 9, 12}

All objects of the set are natural numbers that are multiples of 3.

A = {x : x = 3n, n N and 1n4}

(ii) Let B = {2, 4, 8, 16, 32}

All objects of the set are natural numbers that are powers of 2.

B = {x : x = 2n, nN and 1n5}

(iii) Let C = {5, 25, 125, 625}

All objects of the set are natural numbers that are powers of 5.

C = {x : x = 5n, nN and 1n4}

(iv) Let D = {2, 4, 6,....}

All objects of the set are even natural numbers.

D = {x : x is an even natural number}

(v) Let E = {1, 4, 9, ......., 100}

All objects of the set are perfect squares.

D = {x : x = n2 and 1n10}


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