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On the set N of all natural numbers, a r...

On the set `N` of all natural numbers, a relation `R` is defined as follows: `n R m ` <=> Each of the natural numbers `n` and `m` leaves the same remainder less than 5 when divided by 5. Show that `R` is an equivalence relation. Also, obtain the pairwise disjoint subsets determined by `R` .

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RD SHARMA ENGLISH-RELATIONS-All Questions
  1. Given a non-empty set X , consider P\ (X) which is the set of all subs...

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  2. Let R be the equivalence relation in the set A={0,\ 1,\ 2,\ 3,\ 4,\ 5}...

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  3. On the set N of all natural numbers, a relation R is defined as follow...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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