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`m` is said to be related to `n` if `m` and `n` are integers and `m-n` is divisible by 13. Does this define an equivalence relation?

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Let Z be the set of all integers and R be the relation on Z defined by R= { (a,b): a, b in Z and (a-b) is divisible by 5} . Prove that R is an equivalence relation

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RD SHARMA ENGLISH-RELATIONS-All Questions
  1. An integer m is said to be related to another integer n if m is a mult...

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  2. Show that the relation geq on the set R of all real numbers is r...

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  3. m is said to be related to n if m and n are integers and m-n is divisi...

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

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  5. Show that the relation R defined by R={(a , b):a-b is divisible ...

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  6. Prove that a relation R on a set A is symmetric iff R=R^-1

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  7. Three relations R1, R2a n dR3 are defined on set A={a , b , c} as foll...

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  8. Let a relation R1 on the set R of real numbers be defined as (a , b) ...

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  9. Let S be the set of all points in a plane and R be a relation on S def...

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  10. The following relation is defined on the set of real number: a R ...

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  11. Prove that every identity relation on a set is reflexive, but the c...

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

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  13. Let N denote the set of all natural numbers and R be the relation on N...

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  14. Let N be the set of all natural numbers and let R be a relation on N×N...

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  15. Let R be a relation on the set of all line in a plane defined by (l1, ...

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  16. Each of the following defines a relation on N:x -> y , (i) x , y in N...

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  17. Let A={a , b , c) and the relation R be defined on A as follows: R={(a...

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  18. Given the relation R={(1,2),(2,3) on the set A={1,2,3}, add a minimum ...

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  19. Let A={1,2,3,ddot,9} and R be the relation in AxA defined by (a ,b)R(c...

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  20. Prove that the relation R on the set NxxN defined by (a ,\ b)R\ (c ,\ ...

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