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Prove that the operation @ on QQ defined...

Prove that the operation `@` on `QQ` defined by `x@y=(x-2)/(y-2)` for all `x,yinQQ` does not represent a binary operation on `QQ`.

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Prove that the binary operation @ defined on QQ by a@b=a-b+ab for all a,b in QQ is neither commutative nor associative.

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The operation @ is defined by a@b=b^(a) on the set Z={0,1,2,3,…} . Prove that @ is not a binary opeartion on Z.

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CHHAYA PUBLICATION-BINARY OPERATION-EXERCISE 3(Very Short Answer Type Questions)
  1. Define an associative binary operation on a non-empty set S.

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  2. Let ** and @ be two binary operations on a non-empty setA. Then write ...

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  3. Let P(A) be the power set of a non-empty set A. Prove that union (cup)...

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  4. Let ** be an operation defined on NN, the set of natural numbers, by ...

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  5. Let @ be an operation defined on RR. The set of real numbers, by a@b=m...

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  6. The operation @ is defined by a@b=b^(a) on the set Z={0,1,2,3,…}. Prov...

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  7. Let A={3x+sqrt5y:x,yinZZ}. Show that an operation ** on A defined by, ...

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  8. Prove that the operation 'addition' on the set of irrational numbers i...

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  9. Prove that the operation @ on QQ, the set of rational numbers, defined...

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  10. Let ** be an opeartion defined on S={1,2,3,4} by a**b=m where m is the...

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  11. An operation ** is defined on the set of real numbers RR by a**b=ab+5 ...

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  12. Let S={0,1,2,3,4}, if a,binS, then an operation ** on S is defined by,...

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  13. Let M(2) be the set of all 2xx2 singular matrices of the form {:((a,a)...

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  14. An operation ** on the set of all complex numbers CC is defined by z(...

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  15. Show that an operation ** on RR, the set of real numbers, defined by a...

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  16. Examine whether the operation @ on ZZ^(+) defined by a@b=|a-b| for all...

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  17. Prove that the operation ^^ on RR defined by x^^y= min. of x and y for...

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  18. Prove that the operation ** on ZZ defined by a**b=a|b| for all a,binZZ...

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  19. Prove that the operation @ on QQ defined by x@y=(x-2)/(y-2) for all x,...

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  20. An operation ** is defined onNN as a**b=HCF(a,b) for all a,binNN. Show...

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