Show that A cap B=A cap C need not imply B = C

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1.Set Theory

easy

Show that $A \cap B=A \cap C$ need not imply $B = C$

Option A

Option B

Option C

Option D

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, $B \ne C\,[2 \in B$ and $2 \notin C]$

Standard 11

Mathematics

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