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State whether the following statement is...

State whether the following statement is true or false. Justify:For an arbitrary binary operation `*` on a set `N`, `a * a = a`, `for all a in N`

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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Show that the number of binary operations on {1, 2} having 1 as identi...

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  2. let A = N xxN and * be the binary operation on A defined by : (a,b) * ...

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  3. State whether the following statement is true or false. Justify:For an...

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  4. State whether the following statements are true or false. Justify. If ...

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  5. State whether the following statements are true or false. Justify . Fo...

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  6. Consider a binary operation * on N defined as a* b = a^3 + b^3. Then

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

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  8. Let f : W to W be defined as f(n) =n-1, if n is odd and f(n) = n+1, i...

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  9. If f : R rarr R is defined by f(x) = x^2 - 3x + 2, find f(f(x)).

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  10. Show that the function f : Rrarr {x in R : – 1 < x < 1} defined by 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. Give examples of two functions f : NrarrZ and g : ZrarrZ such that g ...

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  13. Give examples of two functions f : NrarrN and g : NrarrN such that g o...

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

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

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

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

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

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

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

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