MathDB
Putnam 1971 B1

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April 6, 2022
college contests

Problem Statement

Let SS be a set and let ∘\circ be a binary operation on SS satisfying two laws x∘x=x for all x in S, andx\circ x=x \text{ for all } x \text{ in } S, \text{ and} (x∘y)∘z=(y∘z)∘x for all x,y,z in S.(x \circ y) \circ z= (y\circ z) \circ x \text{ for all } x,y,z \text{ in } S. Show that ∘\circ is associative and commutative.
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