Question
Let and be the sets such that and . Show that
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Text solutionVerified
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
.
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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Question Text | Let and be the sets such that and . Show that |
Answer Type | Text solution:1 |
Upvotes | 150 |