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# Show that A ∩ B = A ∩ C need not imply B = C.

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

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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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