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Given a non - empty set, X , consider th...

Given a non - empty set, X , consider the binary operation ** :` P(X) xxP(X) rarr P(X)` given by `A **B = Acap B , AAA,B in P(X)` , where P(X) is the power set X. Show that X is the identity element for this operation and X is the only invertible element in P(X) with respect to the operation ** .

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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
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  2. Given a non empty set X, consider P(X) which is the set of all subsets...

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

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  4. 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. Consider the binary operations * : R xx R to R and o: R xx R to R def...

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

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

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

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

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