Question

Which set of numbers could be the universal set for the sets given below?

(i) A = set of multiples of 5, B = set of multiples of 7.
C = set of multiples of 12

(ii) P = set of integers which are multiples of 4. T = set of all even square numbers.1

Answer 1

(i) We have,

A = set of multiples of 5 = {5, 10, 15, ...}; B = set of multiples of 7 = {7, 14, 21, ...}; and C = set of multiples of 12 = {12, 24, 36, ...}

The universal set for the sets A, B and C can be set of natural numbers, i.e. N.

Disclaimer: The Universal set for the sets A, B and C can be set of whole numbers, integers, rational number of real numbers and so on.

(ii) We have,

P = set of integers which are multiples of 4 = {4, 8, 12, ...}; and T = set of all even square numbers = {4, 16, 36, 64, 100, ...}

So, P can be the Universal set for the sets P and Q.

Disclaimer: Here also, the Universal set can be vary from the ablove.