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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 associative or commutative?

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* on `Q` defined by `a`*`b=(a+b)/2` for all `a ,\ b in Q`
To check commutative
Let `a,b in S`
Then
`a`*`b=(a+b)/2`
`a`*`b=(b+a)/2`
...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Let '*' be a binary operation on N given by a*b=LdotCdotMdot(a , b) fo...

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

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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 binar...

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

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

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

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  8. Check the commutativity and associativity of O on Q defined by a\ \...

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

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

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

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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=...

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

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

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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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