Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C. Show that B = C.

It is given in the question that,

And,

We have to show that, B = C

Let us now assume,

So,

∴

Now, when then:

∴

As,

So,

∴

∴

Similarly, it can be shown that C ⊂ B

Hence, B = C