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Let Z be the set of all integers and R b...

Let Z be the set of all integers and R be the relation on Z defined as `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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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Fill in the blank: The total number of injective functions that can ...

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  2. Fill in the blank: Let R1 be the set of all reals except 1 and * be ...

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  3. Let Z be the set of all integers and R be the relation on Z defined as...

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  4. Fill in the blank: Let f : R rarr R be defined by f(x) = (1)/(2 + c...

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  5. If relation R defined on set A is an equivalence relation, then R is

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  6. True or False statements : Let R = (3,1), (1,3), (3,3) be a relation...

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  7. Are the following statement true or false ? Justify the answer : Every...

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  8. True or False statements : Every function is invertible.

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  9. True or False statements : The relation R = (a,b), (ba,) on the set ...

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  10. Let A be a finite set. Then, each injective function from A into itsel...

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  11. True or False statements : Let A = (a,b,c) and R = (a,b),(a,c). Then...

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  12. The relation R on the set A = {1, 2, 3} defined as R = {(1, 1), (1, 2)...

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  13. The function f : R rarr R defined by f(x) = 1 + x^2 is :

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  14. Every relation which is symmetric and transitive is also reflexive.

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  15. True or False statements : Let N be the set of natural numbers. Then...

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  16. True or False statements : A binary operatio on a set has always the...

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  17. The function f : R rarr R defined by f(x) = 1 + x^2 is :

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  18. True or False statements : Let N be the set of natural numbers. Then...

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  19. True or False statements : The function f : R rarr R defined by f(x)...

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  20. Let A = {0, 1} and N be the set of natural numbers. Then the mapping f...

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