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

Determine whether `*` on `N` defined by `a*b=1` for all `a ,\ b in N` is associative or commutative?

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We have given that * is a binary operation on N defined by `a`*`b = 1` for all `a,b in N`
As we know that commutative property is `p`*`q = q`*`p`
Let’s check the commutativity of given binary operation:
`implies a`*`b = 1`
`implies b`*`a = 1`
`implies b`*`a = a`*`b`
Hence it is commutative.
Now as associative property is `(p`*`q)`*`r = p`*`(q`*`r)`
...
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