Exercise 4

Suppose that you would like to prove the following implication:

For all numbers $n$, if $n$ is prime then $n$ is solitary.

Write out the beginning and end of the argument if you were to prove the statement,

1. Directly

2. By contrapositive

3. By contradiction

You do not need to provide details for the proofs (since you do not know what solitary means). However, make sure that you provide the first few and last few lines of the proofs so that we can see that logical structure you would follow.