Question

Show that `A nn B=A nn C` need not imply `B=C`

Answer 1

Let A,B and C are three sets such that
`A = {a,b},B={b,c}`
and `C = {b,d}`
Here `A cap B = {a,b} cap {b,c} ={b}`
and `A cap C = {a,b}cap {b,d} = {b}`
Therefore, `A cap B = {b} = A cap C`
but we see that `B ne C`
Therefore, `A cap B = A cap C` need not imply `B = C`.