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Define an equivalence relation....

Define an equivalence relation.

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The correct Answer is:
An Relation is said to be equivalence relation if it is reflexive, symmetric and transitive .
For a Relation in R to R

A Relation is said to be an Equivalence relation if it is an

Reflexive : `(a,a) in R` i.e every element is related to itself.

symmetric :if `(a,b)in R ` then `(b,a) in R` must also exist.

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RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Define a symmetric relation.

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  2. Define a transitive relation.

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  3. Define an equivalence relation.

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  4. If A={3,\ 5,\ 7} and B={2,\ 4,\ 9} and R is a relation given by is les...

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  5. A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7} and if R={(x ,\ y): y is one half of x ;...

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  6. Let A={2,\ 3,\ 4,\ 5} and B={1,3,\ 4} . If R is the relation from A to...

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  7. State the reason for the relation R on the set {1, 2, 3} given by R={(...

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  8. Let R={(a ,\ a^3): a is a prime number less than 5} be a relation. Fin...

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  9. Let R be the relation in the set Z of integers given by R={(a,b):2 div...

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  10. For the set A={1,\ 2,\ 3} , define a relation R on the set A as follow...

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  11. Let A={0,\ 1,\ 2,\ 3} and R be a relation on A defined as R={(0,\ 0),\...

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  12. If the relation R be defined on the set A={1,2,3,4,5} by R={(a,b): |a^...

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  13. Let the relation R be defined in N by aRb, if 2a + 3b = 30. Then R = …...

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  14. Write the smallest equivalence relation on the set A={1,\ 2,\ 3} .

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  15. Let R be a relation on the set N given by R={(a ,\ b): a=b-2,\ b >6}do...

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  16. Which of the following is not an equivalence relation on Z ? a\ R\ b...

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  17. R is a relation on the set Z of integers and it is given by (x ,\ y) i...

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  18. Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the ...

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  19. Let R be the relation over the set of all straight lines in a plane ...

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  20. LetA = {1, 2, 3}Then number of relations containing (1, 2) a n d (1, 3...

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