Question

Show that 

A ∩ B = A ∩ C 

need not imply B = C. 

Answer 1

Let A = {0, 1}, B = {0, 2, 3}, and C = {0, 4, 5} 

Accordingly, A ∩ B = {0} and A ∩ C = {0} 

Here, A ∩ B = A ∩ C = {0} 

However, 

B ≠ C [2 ∈ B and 2 ∉ C]