Discrete Math › Section B · Logic and proofs › Topic B.4
Direct proof, contrapositive, and contradiction
A proof is an argument that leaves no case unchecked. Three logical skeletons, the direct, contrapositive and contradiction methods, carry most proofs you will write, and each starts from definitions written in exact form.
In this topic
- What a proof is
- Definitions in usable form
- Direct proof
- Worked example: a direct proof about divisibility
- Proof by contrapositive
- Worked example: proof by contrapositive
- Proof by contradiction
- Worked example: the square root of 2 is irrational
- Cases, existence and counterexamples
- Writing proofs well
- Common mistakes to avoid
- Key takeaways
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