P4.1.1 - Proof by contradiction

Proof by contradiction Including proof of the irrationality of 2 and the infinity of primes, and application to unfamiliar proofs.

Use proof by contradiction to connect the rule to the data and decision in the question.

This matters because proof by contradiction determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply proof by contradiction to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Proof by contradiction is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.