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Prove that every identity relation on...

Prove that every identity relation on a set is reflexive, but the converse is not necessarily true.

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Let `A={a,b,c}`

Let `I_ A` ​ is an identity relation of `A`.

Then, `I_ A ​ ...
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RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Let S be the set of all points in a plane and R be a relation on S def...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Let S be a relation on the set R of all real numbers defined by S=...

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  17. Write the domain of the relation R defined on the set Z of integers as...

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  18. If R and S are transitive relations on a set A , then prove that...

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  19. Let R be the equivalence relation in the set A={0,1,2,3,4,5} given ...

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  20. If R={(x,y):x+2y=8} is a relation on N, write the range of R.

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