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Question
For any two sets of A and B, prove that:
\[B' \subset A' \Rightarrow A \subset B\]
Solution
\[\text{ Let }a \in A . \]
\[ \Rightarrow a \not\in A'\]
\[ \Rightarrow a \not\in B' \left( \because B' \subset A' \right)\]
\[ \Rightarrow a \in B\]
\[\text{ Hence }, A \subset B .\]
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