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Let R(1) be a relation defined by R(1...

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

A

an equivalence relation on R

B

transitive but not reflexive and symmetric

C

symmetric, transitive but nor reflexive

D

neither transitive nor reflexive but symmetric

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

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

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

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

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  5. The void relation on a set A is

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

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

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

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

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

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

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

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

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

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  16. If R be a relation lt from A = {1, 2, 3, 4} to B = {1, 3, 5}, i.e. (a,...

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

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

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

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  20. Let A = {p, q, r}. Which of the following is not an equivalence relati...

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