Let e1,…,en be semilines on the plane starting from a common point. Prove that if there is no u≡0 harmonic function on the whole plane that vanishes on the set e1∪⋯∪en, then there exists a pair i,j of indices such that no u≡0 harmonic function on the whole plane exists that vanishes on ei∪ej. Miklos Schweitzerfunctionreal analysis