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Determine whether * on Q defined by a*b=...

Determine whether `*` on `Q` defined by `a*b=(a+b)/2` for all `a ,\ b in Q` is commutative?

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RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
  1. Let '*' be a binary operation on N given by a*b=LdotCdotM(a , b) for a...

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  2. Determine whether * on N defined by a * b=1 for all a ,\ b in N is ...

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  3. Determine whether * on Q defined by a*b=(a+b)/2 for all a ,\ b in Q i...

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  4. Let A be any set containing more than one element. Let * be a binary...

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  5. Check the commutativity of * on Z defined by a*b=a+b+a b for all a ,\ ...

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  6. Check the commutativity of * on N defined by a*b=2^(a b) for all a ,\ ...

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  7. Check the commutativity of * on Q defined by a*b=a-b for all a ,\ b in...

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  8. Check the commutativity of O on Q defined by a\ \ b=a^2+b^2 for all a ...

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  9. Check the commutativity and associativity of * on Q defined by a * ...

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  10. Check the commutativity of * on Q defined by a*b=a b^2 for all a ,\ b ...

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  11. Check the commutativity of * on Q defined by a*b=a+a b for all a ,\ b ...

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  12. Check the commutativity and associativity of * on R defined by a*b=...

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  13. Check the commutativity of * on Q defined by a*b=(a-b)^2 for all a ,\ ...

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  14. Check the commutativity and associativity of * on Q defined by a*b=...

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  15. Let *, be a binary operation on N, the set of natural numbers defined ...

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  16. Check the commutativity and associativity of * on Z defined by a*b=a...

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  17. Check the commutativity and associativity of * on Q defined bya*b= (...

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  18. Check the commutativity and associativity of * on Z defined bya*b= a...

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  19. Check the commutativity and associativity of * on N defined by a*b=g...

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  20. Let S be the set of all rational number except 1 and * be defined ...

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