Q9. Using properties of sets, show that

(ii) A \cap ( A \cup B ) = A

Answers (1)

This can be solved as follows

(ii) A \cap ( A \cup B ) = A

   A \cap ( A \cup B ) =  (A \cap A) \cup ( A \cap B ) 

   A \cap ( A \cup B ) =  A \cup ( A \cap B )                          {  A \cup ( A \cap B ) = A  proved in 9(i)}

   A \cap ( A \cup B ) =   A

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