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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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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Give examples of two functions f : NrarrZ and g : ZrarrZ such that g ...

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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 * : R xx R to R and o: R xx R to R def...

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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, 3...

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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. Fill in the blank: The number of relations that can be defined from ...

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  17. Let the relation R be defined in N by aRb if 2 a + 3 b = 30. Then R = ...

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  18. Fill in the blank: Consider the set A = (0,1,2) and let R = (0,1), (...

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  19. Let the relation R be defined on the set A={1,2, 3,4,5}" by "R={(a, ...

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  20. Fill in the blank: The identity relation on any non-empty set is alw...

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