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Consider the set S={1,\ omega,\ omega^2}...

Consider the set `S={1,\ omega,\ omega^2}` of all cube roots of unity. Construct the composition table for multiplication `(xx)` on `Sdot` Also, find the identity element for multiplication on `Sdot` Also, check its commutativity and find the identity element. Prove that every element of `S` is invertible.

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RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
  1. Let * be the binary operation on N defined by a*b=H C F of a and b ....

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

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

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

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

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  6. Consider the infimum binary operation ^^ on the set S={1,\ 2,\ 3,\ ...

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Write the multiplication table for the set of integers modulo 5.

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  20. Consider the binary operation * and o defined by the following t...

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