Question: (Two paths) Prove that in every tree T, any two paths of maximum length have a node in common. (I.e. if v0,v1,...,vk and w0,w1,...,wk are

(Two paths) Prove that in every tree T, any two paths of maximum length have a node in common. (I.e. if v0,v1,...,vk and w0,w1,...,wk are paths of maximum length in a tree T, then there are integers i,j {0,1,...,k} such that vi = wj.)

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