Key Concepts: Inductive Reasoning and Conjecture

Inductive Reasoning

Inductive reasoning uses patterns and observations to form a general conclusion called a conjecture. You look at specific cases and make an educated guess about what is always true.

• Example: 2, 4, 6, 8, ... → Conjecture: the next number is 10.
• Inductive reasoning does NOT prove something is true — it only suggests it might be.

Conjecture

A conjecture is an unproven statement based on observations. A conjecture remains unproven until it is shown to be either true (via a proof) or false (via a counterexample).

Counterexample

A counterexample is a single example that disproves a conjecture. You only need ONE counterexample to prove a conjecture is false.

• Conjecture: "All prime numbers are odd." Counterexample: 2 is prime and even.