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Given a non empty set X, consider P(X) w...

Given a non empty set X, consider `P(X)` which is the set of all subsets of X. Define the relation R in `P(X)` as follows: For subsets A, B in P(X), ARB if and only if `A sub B`. Is R an equivalence relation on P(X)? Justify your answer.

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MODERN PUBLICATION-RELATIONS AND FUNCTION-EXAMPLE
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  2. Give examples of two functions f : NrarrN and g : NrarrN such that g o...

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

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  4. Given a non - empty set, X , consider the binary operation ** : P(X) x...

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  5. Find the number of all onto functions formthe set {1,2,3,….,n} to itse...

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

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

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  8. Consider the binary operations * : RxxRrarrR and o : RxxRrarrR define...

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  9. Given a non-empty set X, let * : P(X)xxP(X)rarrP(X), be defined as A *...

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  10. Define a binary operation * on the set {0,1,2,3,4,5} as a*b = {:{(a+...

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  11. Let A = {– 1, 0, 1, 2}, B = {– 4, – 2, 0, 2} and f, g : A rarr B, be f...

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  12. Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, ...

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  13. Let A = {1, 2, 3} Then number of equivalence relations containing (1,...

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  14. Let f : R to R be the signum function defined as f(x) = {{:(1, x gt 0...

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  15. Number of binary operations on theset (a,b) is

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  16. Show that if A= { 1,2,3} and R ={(1,1),(2,2),(3,3) (1,2),(2,1),(2,3),...

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  17. Let R be the quivalence relation in the set Z of integerx given by: R ...

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  18. If A = {1,2,3} and f,g are relations corresponding to the subset of A ...

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

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  20. Show that the function f : R rarr R defined by : f(x) = x/(x^2+1) AA ...

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