IMO Shortlist 1996 problem C7

  Avg: 0,0
  Avg: 9,0
Dodao/la: arhiva
2. travnja 2012.
let V be a finitive set and g and f be two injective surjective functions from VtoV.let T and S be two sets such that they are defined as following
S = \{w \in V: f(f(w)) = g(g(w))\}
T = \{w \in V: f(g(w)) = g(f(w))\}
we know that S \cup T = V, prove:
for each w \in V : f(w) \in S if and only if g(w) \in S
Izvor: Međunarodna matematička olimpijada, shortlist 1996