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Question
For any two sets, prove that:
\[A \cup \left( A \cap B \right) = A\]
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Solution
\[LHS = A \cup \left( A \cap B \right)\]
\[ \Rightarrow LHS = \left( A \cup A \right) \cap \left( A \cup B \right) \]
\[ \Rightarrow LHS = A \cap \left( A \cup B \right) \left( \because A \subset A \cup B \right)\]
\[ \Rightarrow LHS = A = RHS\]
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