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Let f: X rarr Y, be a function. Define a...

Let `f: X rarr Y`, be a function. Define a relation `R` in `X` given by: `R={(a, b): f(a)=f(b)}` Examine if `R` is an equivalence relation.

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V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. If R1 and R2 are equivalence relations in a set A, show that R1 nn R2 ...

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  2. Let X={1,2,3,4,5,6,7,8,9}. Let R1 be a relation in X given by R1={(x, ...

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  3. Let f: X rarr Y, be a function. Define a relation R in X given by: R={...

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  4. Determine which of the following binary operation on the set R are ass...

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  5. Find the number of all one-one functions from set A={1,2,3} to itself.

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  6. Consider the identity function, IN: N rarr N defined as In(x)=x forall...

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

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  8. Let f:RrarrR be defined as f(x) = 10x+7 Find the function g:RrarrR s...

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  9. Let f:WrarrW be defined as f(n) = n-1 if n is odd and f(n) = n+1 i...

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  10. If f:RrarrR is defined by f(x) = x^2-3x+2, find f(f(x))

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  11. Show that the function f:R rarr R given by f(x)=x^3 is injective.

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  12. Given a non empty set X, consider P(X) which is the set of all subsets...

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  13. Find the number of all onto functions from the set {1,2,3 …... n}to i...

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  14. Let S={a, b, c} and T={1,2,3}, Find F^-1 of the following functions F ...

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  15. Let A={-1,0,1,2,} B={-4,-2,0,2} and f, g: A rarr B be functions define...

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  16. Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C)20 ...

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  17. Show that the relation R on the set N xx N defined by (a, b)R(c, d)...

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  18. If f: R rarr R be a function defined by f(x)=4 x^3-7, show that the fu...

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  19. Consider the binary operation ast : QtoQ where Q is the set of rationa...

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  20. Prove that the function f: Q rarr Q given by f(x)=2 x-3 for all x in Q...

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