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Let A=NNxxNN, a binary operation ** is d...

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.

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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 A=RR_(0)xxRR where RR_(0) denote the set of all non-zero real numbers. A binary operation ** is defined on A as follows: (a,b)**(c,d)=(ac,bc+d) for all (a,b),(c,d)inRR_(0)xxRR. Binary operation ** is--Identity element in A is--

Let A=RR_(0)xxRR where RR_(0) denote the set of all non-zero real numbers. A binary operation ** is defined on A as follows: (a,b)**(c,d)=(ac,bc+d) for all (a,b),(c,d)inRR_(0)xxRR. The inveritible elements in A is---

The binary operation ** defined on NN by a**b=a+b+ab for all a,binNN is--

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 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.

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CHHAYA PUBLICATION-BINARY OPERATION-EXERCISE 3 (Long Answer Type Questions)
  1. Construct the composition table for the binary operation multiplicatio...

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  2. A binary operation ** on NN is defined by a**b=L.C.M.(a,b) for all a,...

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  3. Let P(A) b the power set of non-empty set A. A binary operation ** is ...

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  4. A binary operation ** is defined in QQ(0), the set of all non-zero rat...

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  5. Let P(C ) be the power set of non-empty set C. A binary operation ** ...

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  6. Let A=Ncup{0}xxNNcup{0}, a binary operation ** is defined on A by. (a,...

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  7. Let A={0,1,2,3,4,5} be a given set, a binary operation @ is defined on...

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  8. Let A=NNxxNN, a binary operation ** is defined on A by (a,b)**(c,d)=(a...

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  9. Find the values of (i) 4+(6)2 (ii) 7+(5)7 (iii) 5+(8)2 (iv) 3xx(7)...

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  10. Let M(2)(x)d={:{((x,x),(x,x)):},x inRR} be the set of 2xx2 singular ma...

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  11. Prepare the composition table for addition modulo 6 (+(6)) on A={0,1,2...

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  12. Prepare the composition table for multiplication modulo 6 (xx(6)) on A...

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  13. A binary operaiton ^^ on the set A={1,2,3,4,5} is defined by a^^b=min(...

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  14. Let S={1,omega,omega^(2)} be the set of cube roots of unity. Prepare t...

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  15. Prepare the composition table for multiplication (xx) on the set of fo...

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  16. Complete the following nultiplication table so as to define a commutat...

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  17. A binary operation @ is defined on the set A={0,1,2,3,4,5} as follows:...

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  18. An operation ** is defined on the set A={1,2,3,4} as follows: a**b,ab(...

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  19. Let A={1,-1} be the set of square roots of unity. Considering multipli...

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  20. Let ** be the binary defined on the set S={1,2,3,4,5,6} by a**b=r whe...

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