Q. 33.7( 132 Votes )

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

Answer :

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**

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