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Define a commutative binary operation no...

Define a commutative binary operation no a non-empty set A.

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Define an associative binary operation on a non-empty set S.

Define a binary opeartion ** on a non-empty set A.

Complete the following nultiplication table so as to define a commutative binary operation ** on A={1,2,3,4}.

Complete the following multiplication table so as to define a commutative binary operation ** on S={a,b,c,d}

Let ** and @ be two binary operations on a non-empty setA. Then write the condition for which the binary operation ** is distibutive over binary operation @

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 ** 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 a binary on QQ , defined by a**b=(a-b)^(2) for all a,binQQ . Show that the binary operation ** on QQ is commutative but not associative.

Let * be a binary operation defined by a* b = L.C.M , (a,b) AA a,b in N . Show that the binary operation * defined on N is commutative and associative. Also find its identity element of N.

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CHHAYA PUBLICATION-BINARY OPERATION-EXERCISE 3(Very Short Answer Type Questions)
  1. Define a binary opeartion ** on a non-empty set A.

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  2. Define a commutative binary operation no a non-empty set A.

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  3. Define an associative binary operation on a non-empty set S.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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