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Question: problem 1 20 points define multiplication in the set n...

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Problem 1 (20 points). Define multiplication in the set N of natural numbers inductively as 1 . m m and (n + 1) . m = n·m + m for all n, m E N Prove by induction that: (a) n.1-nfor all n E N. i.e., n . 1-1.ni (b) n . (p+q) n . p+ n . q for all n, p, q E N, i.e., the multiplication is distributive: c) n-m-m n for all n, m N, i.e., the multiplication is commutative.

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