Let $A = {1, 2, 3, 4}, B = {1, 2, 3}$ and $C = {2, 4}$ . Find sets X satisfying each pair of conditions. $X \subseteq B, X \neq B$ and $X / \subset C$

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Solution

We have,
$X \subset B, X \neq B$ and $X / \subset C$
$\Rightarrow$ X is a subset of Bother than B itself and X is not a subset of C
$\Rightarrow X ϵ P (B), X / ϵ P (C)$ and $X \neq B$
$\Rightarrow X = {1}, {3}, {1, 2}, {1, 3}, {2, 3}$ .

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