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Prove that a relation R on a set A is sy...

Prove that a relation `R` on a set `A` is symmetric iff `R=R^(-1)` .

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Let suppose that `R=R^(−1)`
Then
`(a,b)∈R`
`=>(b,a)∈R^(−1)`
`=>(b,a)∈R`
Now since R is symmetric.
Therefore `R=R^(−1)` ...
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RD SHARMA-RELATIONS-Solved Examples And Exercises
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  2. Let A be the set of all students of a boys school. Show that the re...

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  3. Prove that a relation R on a set A is symmetric iff R=R^(-1) .

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  4. The relation R on the set N of all natural numbers defined by (x ,\ y)...

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  9. Let a relation R1 on the set R of real numbers be defined as (a ,\ b) ...

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  10. Determine whether Relation R on the set A={1,\ 2,\ 3,\ ,\ 13 ,\ 14} d...

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  11. Determine whether Relation R on the set N of all natural numbers def...

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  12. Determine whether Relation R on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6} defi...

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  13. Determine whether Relation R on the set Z of all integer defined as R=...

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  14. Show that the relation R on R defined as R={(a ,\ b): alt=b} , is refl...

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  15. Let S be the set of all points in a plane and R be a relation on S def...

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  16. Let X={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9} , Let R1 be a relation on X ...

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  17. Show that the relations R on the set R of all real numbers, defined as...

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  18. Let A={1,\ 2,\ 3} . Then, show that the number of relations contain...

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  19. Let A be the set of all human beings in a town at a particular time...

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