Given the sets 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) ϕ

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

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

Question

Philoid · Accepted Answer

(i) Given: A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}

Now, let D = {0, 1, 2, 3, 4, 5, 6}

Since, 8 belongs to C but it is not a member of D.

∴ D is not a universal set for A, B, C.

(ii) Given: A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}

Now, let D = ϕ

Since, D does not contain any element.

∴ D is not a universal set for A, B, C.

(iii) Given: A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}

Now, let D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Since, all the members of A, B, C belongs to D.

∴D is a universal set for A, B, C.

(iv) Given: A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}

Now, let D = {1, 2, 3, 4, 5, 6, 7, 8}

Since, 0 belongs to C but it is not a member of D.

∴ D is not a universal set.

Given the sets 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) ϕ(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}(iv) {1, 2, 3, 4, 5, 6, 7, 8}