Question

For three sets A, B and C, show that $A\cap B=A\cap C$ need not imply $B=C$.

Answer 1

Let's solve this question using an example:

Let us assume $3$ sets such that:

$A=\{1,2,3,4\}$

$B=\{3,4,5,6\}$

$C=\{3,4,7,8\}$.

Then,

$A\cap B=A\cap C=\{3,4\}$ but we can clearly see that $B\ne C$

Hence, $A\cap B=A\cap C$, but $B\ne C$.