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}

(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.


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