For three sets A, B, and C, show that A ∩ B = A ∩ C need not imply B = C.

Question

Philoid · Accepted Answer

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.