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The binary operation * define on N by a*...

The binary operation * define on N by a*b = a+b+ab for all `a,binN` is

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

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.

Prove that the binary operation ** on RR defined by a**b=a+b+ab for all a,binRR is commutative and associative.

On the set Q^+ of all positive rational numbers if the binary operation * is defined by a * b = 1/4ab for all a,b in Q^+ find the identity element in Q^+ .

Discuss the commutativity and associativity of binary operation ** defined on ZZ by the rule a**b=|a|b for all a,binZZ .

Find the identity element of the binary operation ** on ZZ defined by a**b=a+b+1 for all a,binZZ .

A binary operation @ is defined on RR-{-1} by a@b=a+b+ab for all a,binRR-{-1}. (i) Discuss the commutativity and associativity of @ on RR-{-1} . Find the identity element, if exists. (iii) Prove that every element of RR-{-1} is invertible.

Let S be any set containing more than two elements. A binary operation @ is defined on S by a@b=b for all a,binS . Discuss the commutativity and associativity of @ on S.

Let A={0,1,2,3,4,5} be a given set, a binary operation @ is defined on A by a@b=ab(mod6) for all a,bin A. Find the identity element for @ in A . Show that 1 and 5 are the only invetible elements in A.

Prove that the identity element of the binary opeartion ** on RR defined by a**b = min. (a,b) for all a,binRR , does not exist.

CHHAYA PUBLICATION-BINARY OPERATION-EXERCISE 3 (Short Answer Type Questions)
  1. A binary operaiton @ is defined on the set RR-{-1} as x@y=x+y+xy for a...

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  2. If ** be the binary operation on the set ZZ of all integers, defined b...

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  3. A binary operation @ is defined on ZZ, the set of integers, by a@b=|a-...

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  4. Let ** a binary operation on NN given by a**b=H.C.F (a,b) for all a,bi...

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  5. If +(6) (addition modulo 6) is a binary operation on A={0,1,2,3,4,5},...

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  6. A binary operation ** is defined on the set RR(0) for all non- zero re...

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  7. A binary operation ** is defined on the set ZZ of all integers by a@b=...

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  8. A binary operation ** is defined on the set of real numbers RR by a**b...

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  9. For the binary operation multiplication modulo 5*(xx(5)) defined on th...

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  10. A binary operation ** on QQ the set of all rational numbers is defined...

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  11. Prove that the identity element of the binary opeartion ** on RR defin...

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  12. Find the identity element of the binary operation ** on ZZ defined by ...

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  13. The binary operation * define on N by a*b = a+b+ab for all a,binN is

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  14. Prove that 0 is the identity element of the binary operation ** on ZZ^...

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  15. A binary operation ** on QQ(0), the set of all non-zero rational numbe...

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  16. A binary operation @ on QQ-{1} is defined by a**b=a+b-ab for all a,bin...

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  17. A binary operation ** on QQ, the set of rational numbers, is defined b...

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  18. Determine which of the following binary operations are associative and...

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  19. Let S be any set containing more than two elements. A binary operation...

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  20. State whether the following statements are true or false with reasons...

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