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LearnAQA7357First teaching 2017Paper 1 · PureProof

Paper 1 · Module

Proof

2 subtopics≈ 65 min in total

Start the module: Deduction, exhaustion and counterexample Open graphing calculator

Deduction, exhaustion and counterexample
A proof must work for every case, not just the ones you tried. Deduction uses algebra for a general case; exhaustion splits all possibilities into a few cases and checks each; and one single counterexample is enough to show a statement is false.
≈ 30 min
Proof by contradiction
To prove a statement, assume it is false and show that this leads to something impossible. The assumption must have been wrong, so the statement is true. The two famous examples are that $\sqrt2$ is irrational and that there are infinitely many primes.
≈ 35 min