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

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Solution

We have,
$X \subseteq A, X \subseteq B$ and $X \subseteq C$
$\Rightarrow X ϵ P (A), X ϵ P (B)$ and $X ϵ X (C)$
$\Rightarrow$ X is a subset of A, B and C
$\Rightarrow X = ϕ, {2}$ .

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