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Let N^m be the set of al ordered m-tuple...

Let `N^m` be the set of al ordered m-tuples of natral numbers. If x = `(x_1.x_2……x_m)` y = (`y_1,y_2…..y_m)` where `x_i,y_i, in N, I = 1, 2 ….m` and an operation '+' is defined on `N^m` by `x+y = (x_1 + y_1.x_2+y_2,……x_m + y_m)` then prove that given operation is commutative as well as associative.

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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Let '*' be a binary operation on Q defined by a * b = (3ab)/5. Show th...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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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