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 $2 \notin C]$
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