5. Let S be the set of full binary trees, defined recursively as follows: • Basic step: a single vertex v with no edges is a full binary tree T,- • Recursive step: if T, and T, are full binary trees, then a new full binary tree T' can be constructed by taking T1 and T2, adding a new vertex v, and adding edges between v and the roots of T, and T2. Prove that n(T) is odd for any full binary tree T, where n(T) is the number of vertices of T.

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