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Let O be the origin. We define a relatio...

Let `O` be the origin. We define a relation between two points `P` and `Q` in a plane if `O P=O Q` . Show that the relation, so defined is an equivalence relation.

A

partial order relation

B

equivalence relation

C

reflexive but not symmetric

D

reflexive but not transitive

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-CARTESIAN PRODUCT OF SETS AND RELATIONS -Exercise
  1. Let R be a reflexive relation on a set A and I be the identity relatio...

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  2. Let A be the non-void set of the children in a family. The relation 'x...

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  3. Let O be the origin. We define a relation between two points P and ...

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  4. The relation R defined in N as aRbimpliesb is divisible by a is

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  5. Given the relation R={(1,\ 2),\ (2,\ 3)} on the set A={1,\ 2,\ 3} , ad...

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  6. An integer m is said to be related to another integer n, if m is integ...

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  7. Let A = {1, 2, 3, 4}, and let R = {(2, 2), (3, 3), (4, 4), (1, 2)} be ...

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  8. Let R(1) be a relation defined by R(1)={(a,b)|agtb,a,b in R}. Then ...

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  9. Let R be a reflexive relation on a finite set A having n elements and ...

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  10. The void relation on a set A is

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  11. Let R be an equivalence relation on a finite set A having n elements....

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  12. The relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)} on set A={1,2,3} ...

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  13. Let R and S be two equivalence relations on a set A Then : A. R uu S ...

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  14. The relation is subset of on the power set P (A) of a set A is

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  15. Let P={(x,y)|x^(2)+y^(2)=1, x,y in R}. Then, P is

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

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

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

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

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

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