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Let A = N xx N being the set of natural...

Let `A = N xx N ` being the set of natural numbers. Let '*' be a binary operation on A defined by `(a,b) * (c,d) = (a+c,b+d). Show that '*' is commutative.

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Let A = N xx N being the set of natural numbers. Let '*' be a binary operation on A defined by (a,b) * (c,d) = (a+c,b+d). Show that '*' is associative.

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Let A = N xx N being the set of natural numbers. Let '*' be a binary operation on A defined by (a,b) * (c,d) = (a+c,b+d). Show that identity element w.r.t '*' does not exist.

Let A = Q xx Q,Q being the set of rationals. Let '*' be a binary operation on A, defined by (a,b) * (c,d) = (ac,ad+b). Show that '*' is associative.

Let A = N xx N , N being the set of natural numbers. Let * : A xx A rarr A be defined as (a,b)*(c,d) = (ad+bc,bd) for all (a,b), (c,d) in A. Show that '*' is commutative

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Let ** be binary operation on N defined by a ** b = HCF of a and b. Show that ** is both commutative and associative.

Let A = Q xx Q , where Q is the set of all rational numbers and * be a binary operaton on A defined by (a,b) * (c,d) = (ac, ad+b) for all (a,b), (c,d) in A. Then find the identify element of * in A.

Let A = N xx N and ∗ be the 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, if any.

Let A = N xx N , N being the set of natural numbers. Let * : A xx A rarr A be defined as (a,b)*(c,d) = (ad+bc,bd) for all (a,b), (c,d) in A. Show that identify element w.r.t. '*' does not exist.

PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Let A = Q xx Q,Q being the set of rationals. Let '*' be a binary opera...

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  2. Let A = Q xx Q,Q being the set of rationals. Let '*' be a binary opera...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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