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In order that a relation R defined on a ...

In order that a relation R defined on a non-empty set A is an equivalence relation, it is sufficient, if R

A

is reflective

B

is symmetric

C

is transitive

D

possesses all the above three properties

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The correct Answer is:
D
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OBJECTIVE RD SHARMA-CARTESIAN PRODUCT OF SETS AND RELATIONS -Exercise
  1. Let P={(x,y)|x^(2)+y^(2)=1,x,yinR}. Then, R, is

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  2. Let R = {(a, a)} be a relation on a set A.Then R is

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  3. Which one of the following relations on R is an equivalence relation?

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  4. Let X be a family of sets and R be a relation on X defined by A is dis...

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  5. If R is an equivalence relation on a set A, then R^-1 is A. reflexiv...

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  6. Let R and S be two non-void relations on a set A. Which of the followi...

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  7. If R be a relation < from A = {1, 2, 3,4) to B = (1,3,5) that is (a, b...

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  8. If R is a relation from a set A to a set B and S is a relation from B ...

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  9. If R sub A xx B and S sub B xx C be two relations, then (SoR)^-1 =

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  10. In the set A = {1, 2, 3, 4, 5}, a relation R is defined by R = {(x, y)...

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  11. 7. Let A= {p, q, r}. Which of the following is an equivalence relation...

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  12. In order that a relation R defined on a non-empty set A is an equivale...

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  13. Let R be a relation on the set N of naturalnumbers defined by nRm <=> ...

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  14. Let R and S be two non-void relations on a set A. Which of the followi...

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

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  16. Let L be the set of all straight lines in the Euclidean plane. Two lin...

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  17. For real numbers x and y, we write x* y, if x - y +sqrt2 is an irratio...

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  18. Let X = {1, 2, 3, 4} and Y = {1, 3, 5, 7,9}. Which of the following is...

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  19. Let n be a fixed positive integer. Define a relation R on the set Z of...

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  20. Let L denote the set of all straight lines in a plane.Let a relation R...

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