Question

Given the set A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set (s) for all the three sets A, B, and C?

(i) {0, 1, 2, 3, 4, 5, 6}

(ii) $\Phi$

(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(iv) {1, 2, 3, 4, 5, 6, 7, 8}

Answer 1

(i) {0, 1, 2, 3, 4, 5, 6} is not a universal set for A, B, C because 8 $\in$ C but 8 is not a member of {0, 1, 2, 3, 4, 5, 6}.

(ii) $\Phi$ is a set which contains no element. So it is not a universal set for A, B, C.

(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is a universal set for A, B, C because all members of A, B, C are present in {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

(iv) {1, 2, 3, 4, 5, 6, 7, 8} is not a universal set for A, B, C because 0 $\in$ C but 0 is not a member of {1, 2, 3, 4, 5, 6, 7, 8}.