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Let A = R xx R and * be a binary operat...

Let `A = R xx R ` and * be a binary operation on A defined by : (a,b) * (c,d) = (A+c,b+d)`. Show that * is commutative and associative. Find the identity element for * on A. Also find the inverse of every element (a,b) `in`A.

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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Let A = N xx N being the set of natural numbers. Let '*' be a binary ...

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  2. Let A = N xx N being the set of natural numbers. Let '*' be a binary ...

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  3. Let A = R xx R and * be a binary operation on A defined by : (a,b) * ...

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  4. Let A= Q xx Q. Let'*' be a binary operation on A defined by: (a, b) * ...

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  5. Let A= Q xx Q. Let'*' be a binary operation on A defined by: (a, b) * ...

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  6. If the operation * defined by a* b =a^2 + b^2 or all real numbers a an...

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

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

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

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

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

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

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

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

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

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

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

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

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

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