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Let * be the binary operation on N de...

Let * be the binary operation on `N` defined by `a*b=H C F` of `a` and `b` . Does there exist identity for this binary operation on `N` ?

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Check commutative
`*` is commutative if `a * ~b=b * a`
`a * b=H C F` of `a b`
`b * a=HCF` of `b` a
Since `a * b=b * a quad forall quad a, b in N`
* is commutative.
Check associative
* is associative if `(a * ~b) * c=a *(~b * c)`
...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Let R0 denote the set of all non-zero real numbers and let A=R0xxR0...

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

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

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

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

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

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

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  8. \begin{tabular}{|l|l|l|l|l|l|} \hline 1 & 1 & 2 & 3 & 4 & 5 \\ \hline ...

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

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

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

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

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

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

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

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

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

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

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  19. For the binary operation xx7 on the set S={1,\ 2,\ 3,\ 4,\ 5,\ 6} ,...

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  20. Find the inverse of 5 under multiplication modulo 11 on Z(11) .

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