# 1.2 Proof Methods

## A Bogus Proof by Contradiction

Which step(s) contain the logical error?

Bogus Claim: $$\sqrt{4}$$ is irrational.

Exercise 1

Explanation

This proof makes the same logical error twice. It claims that since $$n^2$$ is a multiple of 4, then 4 must also be a factor of $$n$$. However, only 2 must be a factor of $$n$$.