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Determine whether O on Z defined by a...

Determine whether O on `Z` defined by `a\ O\ b=a^b` for all `a ,\ b in Z` define a binary operation on the given set or not:

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RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
  1. Let M be the set of all 2X2 real singular matrices . On M , let * be...

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  2. Determine whether * on N defined by a*b=a^b for all a ,\ b in N de...

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  3. Determine whether O on Z defined by a\ O\ b=a^b for all a ,\ b in ...

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  4. Determine whether * on N defined by a*b=a+b-2 for all a ,\ b in N ...

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  5. Determine whether 'xx6' on S={1,\ 2,\ 3,\ 4,\ 5} defined by axx6b= Rem...

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  6. Determine whether '+6' on S={0,\ 1,\ 2,\ 3,\ 4,\ 5} defined by a+6b={a...

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  7. 'o' on N defined by a o b= a b + b a for all a, b∈N define...

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  8. '*' on Q defined by a*b=(a-1)/(b+1) for all a ,\ b in Q define a bina...

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  9. Determine whether or not the definition of * On Z^+ , defined * by a...

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  10. Determine whether or not the definition of * On Z^+ , defined * by ...

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  11. Determine whether or not the definition of * On R , define by a*b=a...

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  12. Determine whether or not the definition of * On Z^+ , define * by a...

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  13. Determine whether or not the definition of * On Z^+ , define * by a...

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  14. Determine whether or not the definition of * On R , define * by a*b=...

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  15. Let * be a binary operation on set of integers I, defined by a*b=2a+b-...

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  16. Is* defined on the set {1,"2,"3,"4,"5}" by "" a * b"="LdotCdotMd...

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  17. Let S={a ,\ b ,\ c} . Find the total number of binary operations on...

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  18. Find the total number of binary operations on {a ,\ b} .

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  19. Prove that the operation * on the set M={[a0 0b]: a ,\ b in R-{0}}...

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  20. Let S be the set of all rational numbers of the form m/n , where m ...

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