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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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`a stackrel{R}{rightarrow} a stackrel{R-}{rightarrow} a`

`b stackrel{R}{rightarrow} b stackrel{R-}{rightarrow} b`

`C stackrel{R} rightarrow C stackrel{R-}rightarrow C`

`R` is robation `A` and is

Let `R` be `{(a, a),(b, b)(c, c)}`

`R^{-}={(a, a),(b, b),(c, c,)`,

`R` is symebic if `R=R^{-1}`

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RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Let O be the origin. We define a relation between two points P and ...

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  2. Show that the relation R defined by R={(a , b):a-b is divisible ...

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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. Three relations R1, R2 and R3 are defined on set A={a , b , c} as foll...

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

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

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  7. The following relations are defined on the set of real number: a ...

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  8. Prove that every identity relation on a set is reflexive, but the c...

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  9. Let R be a relation defined on the set of natural numbers N as R={(...

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  10. Let N denote the set of all natural numbers and R be the relation on N...

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  11. Let N be the set of all natural numbers and let R be a relation on N×N...

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  12. Let R be a relation on the set of all line in a plane defined by (l1, ...

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  13. Each of the following defines a relation on N: x -> y , (i) x , y in ...

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  14. Let A={a , b , c) and the relation R be defined on A as follows: R={(a...

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  15. Given the relation R={(1,2),(2,3) on the set A={1,2,3}, add a minimum ...

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  16. Let A={1,2,3,.....,9} and R be the relation in AxxA defined by (a ,b)R...

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  17. Prove that the relation R on the set NxxN defined by (a ,\ b)R\ (c ,\ ...

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  18. Let n be a positive integer. Prove that the relation R on the set Z o...

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  19. Let "T" be the set of all triangles in a plane with "R" as relation ...

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  20. If R and S are relations on a set A , then prove the following :...

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