Let A, B, and C be the sets such that A\cup B=A\cup C and A\cap B= | Filo
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Class 11

Math

Co-ordinate Geometry

Sets

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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
.
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