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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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NAGEEN PRAKASHAN-RELATIONS AND FUNCTIONS -Exercies 1a
  1. Give an example of a relation. Which is (i) Symmetric but neither r...

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  2. (i) If A= {x,y,z}, B=(1,2,3} and R= {(x,2),(y,3),(z,1),(z,2), then fin...

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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. Prove that the relation R={(x,y): x, y in N and x-y " is divisible by ...

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  5. If A={a,b,c,d}, then on A . (i) write the identity relation I(A) . ...

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  6. Show that the divisibility relation in the set of positive integers is...

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  7. Two points P and Q in a plane are related if OP = OQ, where is a fixed...

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

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  9. (i) Show that in the set of positive integer, the relation ' is greate...

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  10. Show that the relation is congruent to on the set of all triangles ...

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  11. Show that the divisibility relation in the set of positive integers is...

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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 a relation R be defined by relation The R = {(4, 5), (1,4), (4, 6)...

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  14. If A={1,2,3,5}, B={2,4,6,8} and C={4,16,36,39} are three sets and R i...

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  15. Show that the relation R in the set R of real numbers, defined as R={...

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  16. If R and S are two equivalence relations on a set A; then R nn S is al...

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