Proofs and induction

Concepts

• Direct proof 10 exercisesA direct proof of an implication p⇒ q starts from the hypothesis p and, using definitions and previously proved results, chains s…
• Proof by contradiction 10 exercisesA proof by contradiction of a statement p assumes p is false and deduces something absurd from it, so that p must be true.
• Mathematical induction 10 exercisesMathematical induction proves that a property P(n) holds for every integer n≥ n_0: one checks the base case P(n_0) and proves tha…
• Strong induction 10 exercisesStrong induction proves P(n) for every n≥ n_0: after checking the base case P(n_0), one proves P(k+1) assuming P(j) for all j wit…