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

Question:

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

Solution:

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

Accordingly, $A \cap B=\{0\}$ and $A \cap C=\{0\}$

Here, $A \cap B=A \cap C=\{0\}$

However, $B \neq C[2 \in B$ and $2 \notin C]$