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Consider the binary operations * : RxxRr...

Consider the binary operations `* : RxxRrarrR` and `o : RxxRrarrR` defined as `a*b = |a – b|` and `aob = a, forall a, b in R` Show that ∗ is commutative but not associative, o is associative but not commutative. Further, show that ∀ `a, b, c in R`, `a * (b o c) = (a * b) o (a * c)`. [If it is so, we say that the operation ∗ distributes over the operation o]. Does o distribute over ∗? Justify your answer.

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PSEB-RELATIONS AND FUNCTIONS-Exercise
  1. Consider a binary operation ∗ on N defined as a * b = a^3 + b^3 Choose...

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  2. Consider a binary operation ∗ on N defined as a * b = a^3 + b^3 Choose...

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

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  4. Let f : WrarrW, be defined as f (n) = n – 1, if n is odd and f (n) = ...

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

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

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

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

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

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

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  11. Find the number of all one-one functions from set A = {1, 2, 3} to its...

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  12. Let S = {a, b, c} and T = {1, 2, 3}. Find F^–1 of the following funct...

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  13. Let S = {a, b, c} and T = {1, 2, 3}. Find F^–1 of the following funct...

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

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

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

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

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

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

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  20. Number of binary operations on the set {a, b} is :

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