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# 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 :ℝℝ is linear (of the form mx + b).

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#### Solution Preview

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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