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 $2 ∉ C]$