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Let *, be a binary operation on N, the s...

Let *, be a binary operation on N, the set of natural numbers defined by `a*b = a^b`, for all `a,b in N`. is * associative or commutative on N?

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* is defined by `a`*`b=a^b` on the set `N`
Then we have to prove that * is associative.
Now let `a,b,c in N`
Then
`(a`*`b)`*`c=(a^b)`*`c`
`(a`*`b)`*`c=a^b^c ldots (i)`
`a`*(`b`*`c`)`=a`*`(b^c)`
...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Check the commutativity and associativity of * on Q defined by a*b=...

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

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

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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 Q defined by a*b=...

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

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

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

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

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  10. On the set Z of integers a binary operation * is defined by a*b=a b...

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  11. Let S be the set of all real numbers except -1 and let * be an oper...

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  12. Q, the set of all rational number, * is defined by a*b=(a-b)/2 , show ...

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  13. On Z , the set of all integers, a binary operation * is defined by ...

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  14. On the set Q of all rational numbers if a binary operation * is def...

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  15. The binary operation * is defined by a*b=(a b)/7 on the set Q of al...

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  16. On Q , the set of all rational numbers a binary operation * is defi...

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

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

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  19. If * defined on the set R of real numbers by a*b=(3a b)/7 , find the i...

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  20. Find the identity element in set Q^+ of all positive rational numbers ...

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