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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. Let * : Q xx Q rarr Q be defined a as a * b = 1 + ab for all a, b in Q...

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  2. Let '*' be a binary operation on Q defined by a * b = (3ab)/5. Show th...

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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 N^m be the set of al ordered m-tuples of natral numbers. If x = (x...

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  5. Let A be a non-empty set and '*' be a binary operation on P(A), the po...

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  6. Let A be a non-empty set and '*' be a binary operation on P(A), the po...

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  7. Let A = (1,2,3) and B = (a,b). How many relations can be defined form ...

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  8. If R = (1,3),(2,1) is a relation on the set A = (1,2,3), find R^-1

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  9. Write the domain of the relation R (a,a),(a,b),(a,c) defined on the s...

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  10. Write down the range of the relation R = (1,1), (1,2), (3,2), (4,2) de...

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  11. Given set A = {1,2,3}, then the relation : R = {(1,1),(2,2),(3,3)} is ...

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  12. Is the relation R = (a,a), (a,b), (b,b). Transitive on the set A = (a,...

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  13. Write down the identity relation on the set A = (x,y,z)

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  14. If A = {a, b, c, d} then a relation R = {(a, a), (b, b), (c, c), (d, d...

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  15. Is the relation R = (1,1), (2,2), (3,3) transitive on the set A = (1,2...

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  16. Write the domain of the relation R (a,a),(a,b),(a,c) defined on the s...

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  17. Let A = (1,2,3). For x,y in A, let x R y iff x < y. Write down R as a ...

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  18. Write the smallest reflexive relation on the set A = (a,b)

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  19. Let A = {0, 1, 2, 3} and define a relation R on A as follows : R = {...

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  20. Let A = {0, 1, 2, 3} and define a relation R on A as follows : R = {...

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