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Let `R_0` denote the set of all non-zero real numbers and let `A=R_0xxR_0` . If . is a binary operation on `A` defined by `(a ,\ b)*(c ,\ d)=(a c ,\ b d)` for all `(a ,\ b),\ (c ,\ d) in Adot` Show that . is both commutative and associative on `A`

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Let R_0 denote the set of all non-zero real numbers and let A=R_0xxR_0 . If * is a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a c ,\ b d) for all (a ,\ b),\ (c ,\ d) in Adot Find the identity element in A .

Let A=Nuu{0}xxNuu{0} and let * be a binary operation on A defined by (a ,\ b) * (c ,\ d)=(a+c ,\ b+d) for all (a ,\ b),\ (c ,\ d) in Adot Show that * is commutative on Adot

Let A=NxxN , and let * be a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a d+b c ,\ b d) for all (a ,\ b),\ (c ,\ d) in NxxNdot Show that: * is commutative on Adot (ii) * is associative on Adot

Let A=Nuu{0}xxNuu{0} and let * be a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a+c ,\ b+d) for all (a ,\ b),\ (c ,\ d) in Adot Show that * is associative on Adot

Let A=NxNa n d^(prime)*' be a binaryoperation on A defined by (a , b)*(C , d)=(a c , b d) for all a , b , c , d , in Ndot Show that '*' is commutative and associative binary operation on A.

Let A=NxNa n d^(prime)*' be a binaryoperation on A defined by (a , b)*(C , d)=(a c , b d) for all a , b , c , d , in Ndot Show that '*' is commutative and associative binary operation on A.

Let A=NxxN , and let * be a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a d+b c ,\ b d) for all (a ,\ b),\ (c ,\ d) in NxxNdot Show that A has no identity element.

Let A=NxN , and let * be a binary operation on A defined by (a , b)*(c , d)=(a d+b c , b d) for all (a , b),c , d) in NxNdot Show that : '*' is commutative on A '*^(prime) is associative on A A has no identity element.

Let N be the set of all natural numbers and let R be a relation on NxxN , defined by (a ,\ b)R\ (c ,\ d) a d=b c for all (a ,\ b),\ (c ,\ d) in NxxN . Show that R is an equivalence relation on NxxN

Let A=QxxQ and let * be a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a c ,\ b+a d) for (a ,\ b),\ (c ,\ d) in A . Then, with respect to * on Adot Find the invertible elements of A .

RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
  1. Let * be a binary operation on the set Q0 of all non-zero rational...

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  2. On R-[1] , a binary operation * is defined by a*b=a+b-a b . Prove that...

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  3. Let R0 denote the set of all non-zero real numbers and let A=R0xxR0 ...

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  4. Let R0 denote the set of all non-zero real numbers and let A=R0xxR0 ...

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  5. Let * be the binary operation on N defined by a*b=H C F of a and b ....

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  6. Consider the set S={1,\ -1} of square roots of unity and multiplicatio...

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  7. Consider the set S={1,\ omega,\ omega^2} of all cube roots of unity...

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  8. Consider the set S={1,\ -1,\ i ,\ -i} of fourth roots of unity. Con...

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  9. Consider the set S={1,\ 2,\ 3,\ 4} . Define a binary operation * on...

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  10. Consider the infimum binary operation ^^ on the set S={1,\ 2,\ 3,\ ...

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  11. Consider a binary operation * on the set {1, 2, 3, 4, 5} given by t...

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  12. Define a binary operation * on the set A={0,\ 1,\ 2,\ 3,\ 4,\ 5} as ...

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

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  14. Define a binary operation ** on the set A={1,\ 2,\ 3,4} as a**b=a b...

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  15. Construct the composition table for the composition of functions (o...

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  16. Construct the composition table for xx4 on set S={0,\ 1,\ 2,\ 3} .

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  17. Construct the composition table for +5 on set S={0,\ 1,\ 2,\ 3,\ 4}...

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  18. Construct the composition table for xx6 on set S={0,\ 1,\ 2,\ 3,\ 4...

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  19. Construct the composition table for xx5 on Z5={0,\ 1,\ 2,\ 3,\ 4} .

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  20. For the binary operation xx(10) on set S={1,\ 3,\ 7,\ 9} , find the...

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