Question 1+ Let T be a tree. Prove, direct from the denition of tree, that: (a) Every edge of T is a bridge. Hint: If an edge e = {(1, b} e E(T) is

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Question 1+ Let T be a tree. Prove, direct from the definition of tree, that: (a) Every edge of T is a bridge.Hint: If an edge e = {(1, b} e E(T) is not a bridge, is there a path from o, to b thatavoids 8? Why? What does this imply about circuits? (b) Every vertex of T with degree more than 1 is a cut vertex.Hint: If 'u E V(T) has degree 2 or more there must be a path a 61 v 82 b in T for somedistinct a, b E V(T) and 61, 82 E E(T). If ’U is not a cut vertex, is there a path froma to b that avoids 61 and 62? Why? What does this imply about circuits?