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** on ZZxxZZ defined by (a,b)**(c,d)=(a-...

`**` on `ZZxxZZ` defined by `(a,b)**(c,d)=(a-c,b-d)` for all `(a,b),(c,d)inZZxxZZ.`

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The correct Answer is:
Neither commutative nor associative
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Let ** be a binary operation on A=NNxxNN , defined by, (a,b)**(c,d)=(ad+bc,bd) for all (a,b)(c,d)inA . Prove that A=NNxxNN has no identity element.

Let A=NNxxNN , a binary operation ** is defined on A by (a,b)**(c,d)=(ad+bc,bd) for all (a,b),(c,d)inA. Show that ** possesses no identity element in A.

Let A=Ncup{0}xxNNcup{0}, a binary operation ** is defined on A by. (a,b)**(c,d)=(a+c,b+d) for all (a,b),(c,d)inA. Prove that ** is commutative as well as associative on A. Show also that (0,0) is the identity element In A.

Let S=NNxxNNand** is a binary operation on S defined by (a,b)**(c,d)=(a+c,b+d) for all a,b,c,d in NN . Prove that ** is a commutative and associative binary operation on S.

Let S = N xx N and ast is a binary operation on S defined by (a,b)^**(c,d) = (a+c, b+d) for all a,b,c,d in N .Prove that ** is an associate binary operation on S.

Let A=NNxxNNand@ be a binary operation on A defined by (a,b)@(c,d)=(ac,bd) for all a,b,c,dinNN . Discuss the commutativity and associativity of @ on A.

Let N N be the set of natural numbers and R be a relation on N NxxN N defined by, (a,b) R (c,d) to a+d=b+c, for all (a,b) and (c,d) iN N NxxN N . prove that R is an equivalence relation on N NxxN N .

Let Z be the set of all integers and Z_(0) be the set of all non-zero integers. Let a relation R on ZZ xx ZZ_(0) be defined as follows : (a,b) R (c,d) rrArr ad=bc," " for " " all (a,d),(c,d) in ZZxxZZ_(0)

Let A = N xx N and ** be the binary opertion on A defined by (a,b) ** (c,d) = (a + c, b+d) Show that ** is commutative and associative.

Let A=N x N and *be a binary operation on A defined by (a,b)*(c,d) =(a+c,b+d).Show(A*) has on identity element.

CHHAYA PUBLICATION-BINARY OPERATION-EXERCISE 3 (Short Answer Type Questions)
  1. Discuss the commutativity and Associativity ** on QQ defined by x**y=(...

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  2. Discuss the commutativity and associativity ** on RR defined by a**b=|...

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  3. ** on ZZxxZZ defined by (a,b)**(c,d)=(a-c,b-d) for all (a,b),(c,d)inZZ...

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  4. Check commutativity and associativity @ on M(2)(RR) defined by A@B=(1)...

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  5. An operation ** on ZZ, the set of integers, is defined as, a**b=a-b+ab...

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  6. (I) Let ** be a binary operation defined by a**b=2a+b-3. Find 3**4. ...

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  7. A binary operaiton @ is defined on the set RR-{-1} as x@y=x+y+xy for a...

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  8. If ** be the binary operation on the set ZZ of all integers, defined b...

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  9. A binary operation @ is defined on ZZ, the set of integers, by a@b=|a-...

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  10. Let ** a binary operation on NN given by a**b=H.C.F (a,b) for all a,bi...

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  11. If +(6) (addition modulo 6) is a binary operation on A={0,1,2,3,4,5},...

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  12. A binary operation ** is defined on the set RR(0) for all non- zero re...

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  13. A binary operation ** is defined on the set ZZ of all integers by a@b=...

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  14. A binary operation ** is defined on the set of real numbers RR by a**b...

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  15. For the binary operation multiplication modulo 5*(xx(5)) defined on th...

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  16. A binary operation ** on QQ the set of all rational numbers is defined...

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  17. Prove that the identity element of the binary opeartion ** on RR defin...

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  18. Find the identity element of the binary operation ** on ZZ defined by ...

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  19. The binary operation * define on N by a*b = a+b+ab for all a,binN is

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  20. Prove that 0 is the identity element of the binary operation ** on ZZ^...

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