Question

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 universals 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) It can be seen that A \(⊂\) {0, 1, 2, 3, 4, 5, 6}
B \(⊂\) {0, 1, 2, 3, 4, 5, 6}
However, C \(\not\subset\)  {0, 1, 2, 3, 4, 5, 6}

Therefore, the set {0, 1, 2, 3, 4, 5, 6} cannot be the universal set for the sets A, B, and C.

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(ii) \(A \not\subset \phi, B \not\subset \phi, C \not\subset \phi\)

Therefore, \(\phi\) cannot be the universal set for the sets A, B, and C.

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(iii) A \(\subset\) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B \(\subset\) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
C \(⊂\) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Therefore, the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is the universal set for the sets A, B, and C.

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(iv) A \(⊂\) {1, 2, 3, 4, 5, 6, 7, 8}
B \(\subset\) {1, 2, 3, 4, 5, 6, 7, 8}
However, C \(\not\subset\) {1, 2, 3, 4, 5, 6, 7, 8}

Therefore, the set {1, 2, 3, 4, 5, 6, 7, 8} cannot be the universal set for the sets A, B, and C.