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 universal set (s) for all the three sets $A,B$ and $C$
i)$\{0,1,2,3,4,5,6\}$
ii)$\varphi$
iii)$\{0,1,2,3,4,5,6,7,8,9,10\}$
iv)$\{0,1,2,3,4,5,6,7,8\}$

Answer 1

(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, $C\text{/}\subset \{0,1,2,3,4,5,6\}$
Therefore, the set $\{0,1,2,3,4,5,6\}$ cannot be the universal set for the sets A, B and C.
(ii) $A\text{/}\subset \varphi ,B\text{/}\subset \varphi ,C\text{/}\subset \varphi$
Therefore, $\varphi$ 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, $C\text{/}\subset \{1,2,3,4,5,6,7,8\}$
Therefore, the set $\{1,2,3,4,5,6,7,8\}$ cannot be the universal set for the sets A, B, and C.