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Show that the relation R in the set A = (1,2,3,4,5} given by R = {(a,b) : |a - b| is even }, is an equivalence relation. Show that all the elements of {1,3,5} are related to each other and all the elements of {2,4} are related to each other. But no element of {1, 3, 5} is related to any element of {2,4}.

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A N EXCEL PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
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  3. Show that f : N rarr N given by f(x) = { ((x +1), if x is odd), ((x ...

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  4. Consider a function f : [0, pi/2] rarr R given by f(x) = sin x and g...

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  5. Show that the function f : R** rarr R** defined by f (x) = 1/x is one-...

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  6. Check the injective and surjective of the following functions : f : N ...

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  7. Check the injective and surjective of the following functions : f : Z ...

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  8. Check the injective and surjective of the following functions : f : R ...

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  9. Check the injective and surjective of the following functions : f : N ...

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  10. Check the injective and surjective of the following functions : f : Z ...

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  11. Prove that the greatest integer function f : R rarrR given by f(x) =[x...

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  13. Show that the signum function f : R rarr R given by f(x)= {(1,if x gt ...

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  14. Let A = {1, 2, 3}, B { 4, 5, 6} and let f = {(1,4),(2,5)(3,6)} be a fu...

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  15. In each of the following cases, states whether the function is one-one...

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  16. In each of the following cases, states whether the function is one-one...

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  17. Let A and B be sets. Show that f: AxxB to BxxA such that f(a,b) = ...

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  18. Let f: N to N be defined by f(n) = { (((n+1)/2)if n is odd), (n/2 if...

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  19. Let A = R - {-3} and B = R - {1} Consider the function f : A rarr B...

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  20. Let f:R rarrR be defined as f(x) = x^4 Choose the correct answer

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  21. Let f:R rarrR be defined as f(x) = 3x Choose the correct answer

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