Question

For three sets A, B, and C, show that 

A ∩ B = A ∩ C need not imply B = C.

Answer 1

Let 

A = {1, 2} 

B = {2, 3} 

C = {2, 4} 

Then, 

A ∩ B = {2} 

A ∩ C = {2} 

Hence, 

A ∩ B = A ∩ C, but clearly B is not equal to C.