Q3. Let A, B, and C be the sets such that A \cup B = A \cup C and A \cap B = A \cap C. Show that B = C.

       

Answers (1)

Let A, B, and C be the sets such that A \cup B = A \cup C and A \cap B = A \cap C

To prove : B = C.

 A \cup B = A + B - A \cap B =  A \cup C = A + C - A \cap C

   \double \rightarrow \arrow            A + B - A \cap B =  A + C - A \cap C

   \double \rightarrow \arrow                B - A \cap B =   C - A \cap C              ( since  A \cap B = A \cap C )

   \double \rightarrow \arrow                      B = C

Hence proved that  B= C.

 

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