1. Explain the difference between inductive and deductive reasoning.

Inductive reasoning is making a conjecture based on observations or patterns, which may or may not be correct. Deductive reasoning is using logic to make true statements to come to a conclusion in all circumstances.

2. Explain the difference between a “conjecture” and a “theorem”.

A conjecture is the educated guess concluded through inductive reasoning. However, inductive reasoning can never be used to prove a conjecture. A theorem is a logical conclusion that can be proved through deductive reasoning.

3. Explain the difference between an inductive “proof” and a deductive proof.

Inductive proofs are made from educated guesses, so you can never be certain that there isn’t a counterexample. Deductive proofs are made from using logic and can be proved using deductive reasoning, which makes it a theorem.