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Show that an operation ** on RR, the set...

Show that an operation `**` on `RR`, the set of real numbers, defined by `a**b=3ab+sqrt2,` for all `a,binRR`. Is a binary operaion on `RR.`

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Prove that an operation ** on RR , the set of real numbers, defined by x**y=2xy+sqrt5, for all x,yinRR , is a binary operation on RR .

An operation ** is defined on the set of real numbers RR by a**b=ab+5 for all a,binRR . Is ** a binary operation on RR ?.

let ** be a binary operation on RR , the set of real numbers, defined by a@b=sqrt(a^(2)+b^(2)) for all a,binRR . Prove that the binary operation @ is commutative as well as associative.

Let @ be an operation defined on RR . The set of real numbers, by a@b=min(a,b) for all a,binRR . Show that @ is a binary operation on RR .

Prove that the operation @ on QQ , the set of rational numbers, defined by a@b=ab+1 is binary operational on QQ .

A binary operation ** is defined on the set of real numbers RR by a**b=2a+b-5 for all a,bin RR . If 3**(x-2)=20 find x.

An operation ** on ZZ , the set of integers, is defined as, a**b=a-b+ab for all a,binZZ . Prove that ** is a binary operation on ZZ which is neither commutative nor associative.

Let ** be a binary operation on NN , the set of natural numbers defined by a**b=a^(b) for all a,binNN is ** associative or commutative on NN ?

If ** be the binary operation on the set ZZ of all integers, defined by a**b=a+3b^(2) , find 2**4.

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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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