MathDB
Putnam 1972 A2

Source: Putnam 1972

February 17, 2022
PutnamBinary operation

Problem Statement

Let SS be a set with a binary operation ∗\ast such that 1) a∗(a∗b)=ba \ast(a\ast b)=b for all a,b∈Sa,b\in S. 2) (a∗b)∗b=a(a\ast b)\ast b=a for all a,b∈Sa,b\in S. Show that ∗\ast is commutative and give an example where ∗\ast is not associative.
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