Does commutativity imply Associativity?

Does commutativity imply associativity? I’m asking this because I was trying to think of structures that are commutative but non-associative but couldn’t come up with any. Are there any such examples?

NOTE: I wasn’t sure how to tag this so feel free to retag it.

Answer

Consider the operation (x,y)xy+1 on the integers.

Attribution
Source : Link , Question Author : Eugene , Answer Author : marlu

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