MathDB
two injective surjective function

Source: ISL 1996, C7

June 6, 2005
functionsymmetrycombinatoricspartitionIMO Shortlist

Problem Statement

let V V be a finitive set and g g and f f be two injective surjective functions from V VtoV V.let T T and S S be two sets such that they are defined as following" S \equal{} \{w \in V: f(f(w)) \equal{} g(g(w))\} T \equal{} \{w \in V: f(g(w)) \equal{} g(f(w))\} we know that S \cup T \equal{} V, prove: for each w∈V:f(w)∈S w \in V : f(w) \in S if and only if g(w)∈S g(w) \in S
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