Exercise 505Logic, sets and proofs › Proof techniquesHigh schoolAdded 3 Nov 2026

Summary of logic and proof techniques

#summary#proof#logic

Statement

Summarize the key proof techniques.

Hint

Review the main methods.

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Direct proof. Assume hypothesis, derive conclusion step by step.

Contraposition. Prove $\neg Q\Rightarrow\neg P$ instead of $P\Rightarrow Q$ .

Contradiction. Assume the negation of the claim, derive a contradiction.

Cases. Split into exhaustive cases and prove each.

Counterexample. To disprove a universal statement, exhibit one counterexample.

Induction. Base case + inductive step (weak, strong, or structural).

Quantifiers. $\forall$ and $\exists$ ; order matters.

Conclusion. These techniques cover most standard mathematical proofs.