MathCastle
Groups and FieldsMediumGroups and the Group Axioms

Groups and the Group Axioms · Medium problem

How many of these five operations on Z\mathbb Z are associative?   a∗b=a−b\;a*b=a-b,   a∗b=a+b+1\;a*b=a+b+1,   a∗b=max⁡(a,b)\;a*b=\max(a,b),   a∗b=2a+b\;a*b=2a+b,   a∗b=∣a−b∣\;a*b=|a-b|.