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Check the commutativity and associati...

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

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* is defined by `a`*`b=2^(ab)` on the set `N`
Then we have to check that * is associative and commutative or not .
Now let `a,b,c in N`
Then
`(a`*`b)`*`c=(2^(ab))`*`c`
`(a`*`b)`*`c= 2^(2^(ab)c)`
`(a`*`b)`*`c= 2^(2^(ab)c) ldots (i)`
...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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  9. Check the commutativity and associativity of * on R 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. Let *, be a binary operation on N, the set of natural numbers defined ...

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

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

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

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

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

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