Question
The relation and are symmetric in the set , then show that and are symmetric.
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Text solutionVerified
We will prove, union of sets is symmetric
Let
Let
or
or (Since, R and R' are symmetric)
Hence, is symmetric.
Now, we will prove, intersection of sets is symmetric
Let
Let
or
or (Since, R and R' are symmetric)
Hence, is symmetric.
Now, we will prove, intersection of sets is symmetric
Let
Let
and
and (Since, R and R' are symmetric)
Hence, is symmetric.
Let
and
and (Since, R and R' are symmetric)
Hence, is symmetric.
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Question Text | The relation and are symmetric in the set , then show that and are symmetric. |
Answer Type | Text solution:1 |
Upvotes | 150 |