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) ${0, 1, 2, 3, 4, 5, 6, 7, 8}$

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Solution

(i) It can be seen that $A \subset {0, 1, 2, 3, 4, 5, 6}$
$B \subset {0, 1, 2, 3, 4, 5, 6}$
However, $C / \subset {0, 1, 2, 3, 4, 5, 6}$
Therefore, the set ${0, 1, 2, 3, 4, 5, 6}$ cannot be the universal set for the sets A, B and C.
(ii) $A / \subset ϕ, B / \subset ϕ, C / \subset ϕ$
Therefore, $ϕ$ cannot be the universal set for the sets A, B, and C.
(iii) $A \subset {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}$
$B \subset {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}$
$C \subset {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}$
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.
(iv) $A \subset {1, 2, 3, 4, 5, 6, 7, 8}$
$B \subset {1, 2, 3, 4, 5, 6, 7, 8}$
However, $C / \subset {1, 2, 3, 4, 5, 6, 7, 8}$
Therefore, the set ${1, 2, 3, 4, 5, 6, 7, 8}$ cannot be the universal set for the sets A, B, and C.

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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 Ci){0, 1, 2, 3, 4, 5, 6} ii)ϕiii){0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}iv){0, 1, 2, 3, 4, 5, 6, 7, 8}

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) ${0, 1, 2, 3, 4, 5, 6, 7, 8}$