which of the following may be considered as universals set

Tuesday, 8 April 2014
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) Φ
(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(iv) {1, 2, 3, 4, 5, 6, 7, 8}

Answer
(i) All elements which belongs to set A or B or C are 0, 1, 2, 3, 4, 5, 6 and 8.
Any set which contains at least these element will be known as universal set for A,B and C
In given options, option (iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} contains all these elements.
Hence, (iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10} is the correct option.

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