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Question
For any two sets A and B, prove the following:
\[A \cap \left( A' \cup B \right) = A \cap B\]
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Solution
\[LHS = A \cap \left( A' \cup B \right)\]
\[ = \left( A \cap A' \right) \cup \left( A \cap B \right)\]
\[ = \left( \phi \right) \cup \left( A \cap B \right)\]
\[ = A \cap B = RHS\]
Hence proved.
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