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Question
For any two sets A and B, prove that \[\left( A - B \right) \cup \left( A \cap B \right) = A\]
Solution
\[\left( A - B \right) \cup \left( A \cap B \right) = \left( A \cap B' \right) \cup \left( A \cap B \right) \left( X - Y = X \cap Y' \right)\]
\[ = A \cap \left( B' \cup B \right) \left( \text{ Distributive law } \right)\]
\[ = A \cap \cup \]
\[ = A\]
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