Proof Techniques

Use a counterexample to disprove a universal claim quickly. Use contradiction when assuming the opposite of a claim leads to something impossible.

In proof by contradiction, assume the target claim is false and drive the assumption to something impossible, often a parity clash or a definition failure.

When a statement has the form if P, then Q, you need to choose a proof path that preserves logic instead of guessing from examples.

Mathematical induction proves a statement for every integer in a sequence by establishing a base case and an induction step.

When a statement splits naturally into a small number of possibilities, prove each case cleanly and make sure the cases cover everything.

To prove two sets are equal, show both inclusions or use a membership argument with x ∈ A iff x ∈ B.