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Let A = N xx N, N being the set of natur...

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 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 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 identify element w.r.t. '*' does not exist.

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.

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.

Let N be the set of natural number and R be the relation in NxxN defined by : (a,b) R (c,d) iff ad = bc, for all (a,b), (c,d) in NxxN Show that R is an equivalence relation.

Let * : Q xx Q rarr Q be defined a as a * b = 1 + ab for all a, b in Q. Show that * is commutative but not associative.

Let A = Q - (0), where Q is the set of rationals. Let * : A xx A rarr A be defined as a*b = (3ab)/(5) for all a,b in A. Check whetehr * is commutative or associative. Find the identity element for * and inverse of a in A (if it exists).

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 , 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 = Q xx Q , where Q is the set of all natural involved and * be the binary operation on A defined by (a,b)* (c,d) =(ac,b+ad) for (a,b), (c,d) in A. Then find Invertible elements of A, and hence write the inverse of elements (5,3) and (1/2, 4)

PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Let A = N xx N, N being the set of natural numbers. Let * : A xx A rar...

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  2. Let A = (a,b,c) and R be the relation defined on A as follows R = (a,a...

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  3. Let A = (6,7,8,10), B = (2,4,5) a inA , b in B and R be the relation f...

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  4. For the given relation R on a set S, determine which are equivalence r...

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  5. For the given relation R on a set S, determine which are equivalence r...

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  6. For the given relation R on a set S, determine which are equivalence r...

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  7. In the following cases, for the given relation R on the set S, determi...

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  8. In the following cases, for the given relation R on the set S, determi...

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  9. For the given relation R on a set S, determine which are equivalence r...

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  10. Check whether the relation R defined in the set (1, 2, 3, 4, 5, 6) as ...

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  11. Show that R= {(a, b): a ge b} is reflexive and transitive but not sym...

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  12. Let A be the set of human beings living in a town at a particular time...

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  13. Given the relation R = {(1, 2), (2, 3)} on the set of natural numbers,...

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  14. Show that each of the relation R in the set A ={x in z : 0 le x le 12}...

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  15. Show that each of the relation R in the set A = {x in Z : 0 le x le 12...

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  16. Is inclusion of a subset in another, in the context of a universal set...

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  17. If R is a relation in N xx N, show that the relation R defined by (a, ...

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  18. If R is the relation in N xx N defined by (a, b) R (c,d) if and only i...

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  19. Show that the relation R defined by (a, b) R(c,d)implies a+d=b+c in...

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  20. Each of the following defines a relation R in N. x R y if xy is squa...

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  21. Each of the following defines a relation R in N. x R y if xy is squa...

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