Question: Direct proof and proof by cases: (a) Let T be a tree, and let a and b vertices of T which are not adjacent.

Direct proof and proof by cases: (a) Let T be a tree, and let a and b vertices of T which are not adjacent.

Direct proof and proof by cases: (a) Let T be a tree, and let a and b vertices of T which are not adjacent. Prove that adding the edge (a, b) to T gives a graph which contains a cycle. (b) Prove that [32-91+z23 for every z E R. (c) Let a and b be arbitrary integers. Prove that ab + ba is even.

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SOLUTION a Direct Proof To prove that adding the edge ab to T gives a graph containing a cycle we can show that there is a path from vertex a to verte... View full answer

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