Let A, B, and C be the sets such that A\cup B=A\cup C and A\cap B= | Filo

Class 11

Math

Co-ordinate Geometry

Sets

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150

Let and be the sets such that and . Show that

Solution: Let, A, B and C be the sets such that and .
To show:
Let
(By def of union of sets)
()
or
Case I

Also,

()
and

But is an arbitrary element in B.
.....(1)

Now, we will show that .
Let
(by def of union of sets)
()
or
Case I : When
Also,

and

But is an arbitrary element of C.
Hence,       .....(2)

From (1) and (2), w eget
.
635
150

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