Q10. Show that A \cap B = A \cap C need not imply B = C.

Answers (1)

Let,       A = {0,1,2}

             B = {1,2,3}

             C = {1,2,3,4,5}

 Given,   A \cap B = A \cap C

L.H.S :     A \cap B = {1,2}

R.H.S :    A \cap C = {1,2}

and here   {1,2,3} \not = {1,2,3,4,5}  =   B \not = C.

Hence,  A \cap B = A \cap C need not imply B = C.

 

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