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Prove that the relation R on Z defined b...

Prove that the relation `R` on `Z` defined by `(a ,\ b) in RhArr` `a-b` is divisible by 5 is an equivalence relation on `Z` .

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Given as R on Z defined by `(a, b) \in R \Leftrightarrow a-b` is divisible by 5

To prove equivalence relation the given relation should be reflexive, symmetric and transitive.

We have to check these properties on `R`.

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RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Show that the relation R defined by R={(a , b):a-b is divisible ...

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  2. Show that the relation R on the set Z of integers, given by R={(a ,\ b...

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  3. Prove that the relation R on Z defined by (a ,\ b) in RhArr a-b is di...

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  4. Let n be a fixed positive integer. Define a relation R on Z as follows...

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  5. Let Z be the set of integers. Show that the relation R={(a ,\ b): a ,\...

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

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  7. Let R be a relation on the set A of ordered pairs of integers defined ...

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  8. Show that the relation R on the set A={x in Z ;0lt=xlt=12} , given by...

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  9. Let L be the set of all lines in X Y -plane and R be the relation in L...

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  10. Show that the relation R , defined on the set A of all polygons as R={...

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

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  12. Let R be the relation defined on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7}...

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  13. Let S be a relation on the set R of all real numbers defined by S={(a ...

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  14. Let Z be the set of all integers and Z0 be the set of all non-zero int...

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  15. If R and S are relations on a set A , then prove the following: R and ...

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  16. If R and S are transitive relations on a set A , then prove that RuuS ...

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  17. Write the domain of the relation R defined on the set Z of integers as...

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  18. If R={(x ,\ y): x^2+y^2lt=4; x ,\ y in Z} is a relation on Z , write ...

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  19. Write the identity relation on set A={a ,\ b ,\ c} .

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  20. Write the smallest reflexive relation on set A={1,\ 2,\ 3,\ 4} .

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