# Proof Techniques

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Proof Techniques: Homework 03

Provide counterexamples to each of the following.

Every odd number is prime.

Every prime number is odd.

For every real number x, we have x2 > 0.

For every real number x 0, we have 1/x > 0.

Every function f :ℝℝ is linear (of the form mx + b).

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Proof Techniques: Homework 03

Provide counterexamples to each of the following.

(a) Every odd number is prime.

Answer: Not all odd numbers are prime. For example, 9 is an odd number, but it is a composite number, not a prime, because it has a set of factors {1,9} and {3,3}

(b) Every prime ...

#### Solution Summary

The expert provides counterexamples to each proof. This posting contains the solution to the given problem.

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