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Show that the number of binary operation...

Show that the number of binary operations on {1, 2} having 1 as identity and having 2 as the inverse of 2 is exactly one.

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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Let * be a binary operation on the set Q of rational numbers as follow...

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  2. Let ∗ be a binary operation on the set Q of rational numbers as follow...

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  3. Show that the number of binary operations on {1, 2} having 1 as identi...

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

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

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

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

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

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

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

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  12. Show that the function f : Rrarr {x in R : – 1 < x < 1} defined by f(x...

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

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  14. Give examples of two functions f : NrarrZ and g : ZrarrZ such that g ...

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

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

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

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

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

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

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