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Let A be any set containing more than...

Let `A` be any set containing more than one element. Let * be a binary operation on `A` defined by `a*b=b` for all `a ,\ b in Adot` Is * commutative or associative on `A` ?

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Let `a, b in A`
Then, `a` *` b = b`
`b `* `a = a`
So, `a` *` b != b `* `a`
Thus, * is not commutative on A
Let us check associativity:
Let `a, b, c in A`
`a` *` (b` *` c) = a` *` c = c`
...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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  2. Determine whether * on Q defined by a*b=(a+b)/2 for all a ,\ b in Q i...

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  3. Let A be any set containing more than one element. Let * be a binar...

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

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

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

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

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

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

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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 R defined by a*b=...

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  12. Check the commutativity and associativity of * on Q 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. Let *, be a binary operation on N, the set of natural numbers defined ...

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

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

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

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

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

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  20. Show that the binary operation * on Z defined by a*b=3a+7b is not c...

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