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Define a binary operation * on the set {...

Define a binary operation * on the set {0,1,2,3,4,5} as
`a*b = {:{(a+b, if a +b < 6),(a+b-6, if a +bge6):}` Show that zero is the identity for this operation and each element `ane0` of the set is invertible with 6 - a being the inverse of a.

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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Consider the binary operations * : R xx R to R and o: R xx R to R def...

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

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

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

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

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

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

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  8. Number of binary operations on theset (a,b) is

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

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

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

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

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

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  14. Fill in the blank: Let f = (1,2), (3,5), (4,1) and g = (2,3), (5,1),...

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  15. Fill in the blank: If f (X) = 4-(x-7)^3, then f^-1 (x) =

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  16. Fill in the blank: If f = (a,c), (b,d) and g = (c, a), (d,b) then ra...

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  17. Fill in the blank: Let f : R rarr R be defined by f(x) = (x)/(sqrt(1...

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  18. Fill in the blank: Let f : R rarr R be defined by f(x) = (1)/(2 + c...

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  19. Fill in the blank: Let * be a binary operation defined on Z as a * b...

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  20. Consider the set A = {1, 2, 3} and R be the smallest equivalence relat...

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