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Let A be a set having more than one e...

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

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Let’s check the commutativity of given binary operation:
`implies a`*`b=a`
`implies b`*`a=b`
`implies a`*`b!=b`*`a`
Hence it is not commutative.
Let’s check the associativity of given binary operation: `implies (a`*`b)`*`c=(b)`*`c`
`implies (a`*`b)`*`c=b`*`c`
...
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