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Let n be a fixed positive integer. Defin...

Let `n` be a fixed positive integer. Define a relation `R` on `Z` as follows: `(a ,\ b) in RhArra-b` is divisible by `ndot` Show that `R` is an equivalence relation on `Zdot`

A

reflexive

B

symmetric

C

transitive

D

none of these

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

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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 lt from A = {1, 2, 3, 4} to B = {1, 3, 5}, i.e. (a,...

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

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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 natural numbers defined by n\ R\ m...

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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 , define x\ R\ y iff x-y+sqrt(2) is an irrati...

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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 Z as follows...

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

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