Potrebujem nájsť chybu v dôkaze:
ak aspoň jeden chlapec má hnedé vlasy, tak všetci chlapci majú hnedé vlasy.
V(n) pre n=1 je výrok pravdivý
povedzme, že chlapec C1 má hnedé vlasy. Potom v skupine k chlapcov C1,C2...Ck má chlapec C1 hnedé vlasy a podľa indukčného predpokladu všetci chlapci majú hnedé vlasy: (1) C1=C2=...=Ck
Podobne v skupine k chlapcov C1,C2...Ck-1,Ck+1 kde C1 má hnedé vlasy, majú všetci chlapci modré oči: (2 )C1=C2=...=Ck-1=Ck+1
z rovností (1) a (2) vyplýva, C1=C2=...=Ck-1=Ck=Ck+1, čo ale znamená, že všetkých k+1 chlapcov má hnedé vlasy, teda je dokázaná platnosť tvrdenia V(k+1)
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