Proof by Exhaustion and Disproof by Counterexamples

The video tutorial covers proof by exhaustion and disproof by counterexample. It explains proof by exhaustion as a method to verify statements by checking all possible cases, using examples like finding prime numbers between 10 and 20 and identifying perfect squares between 800 and 900. The four colour theorem is discussed as a large-scale application of proof by exhaustion using computers. The tutorial then shifts to disproof by counterexample, illustrating how a single counterexample can invalidate a conjecture, with examples provided for clarity.

How does disproof by counterexample differ from proof by exhaustion?

Provide an example of a conjecture and demonstrate how to disprove it using a counterexample.

What are the limitations of proof by exhaustion in mathematical proofs?