Patterns and Conjectures

Use examples to make and test mathematical claims.

Lesson 1 of 53 parts Practice Flashcards

1/3

Inductive Reasoning

Objective: Form a conjecture from observed cases.

Inductive reasoning uses a pattern of particular observations to propose a general conjecture. A pattern suggests a claim but does not establish it for every case.

Worked examples

Try itThe first three even numbers each have a factor of 2. What might you conjecture?Show answer

Every even integer is divisible by 2; prove the general claim separately.

Swipe sideways to move between sections

Inductive Reasoning

Objective: Form a conjecture from observed cases.

Inductive reasoning uses a pattern of particular observations to propose a general conjecture. A pattern suggests a claim but does not establish it for every case.

Worked examples

Try itThe first three even numbers each have a factor of 2. What might you conjecture?Show answer

Every even integer is divisible by 2; prove the general claim separately.

Counterexamples

Objective: Disprove a universal claim with one valid case.

A counterexample is one instance satisfying the stated conditions for which a universal conclusion is false. It disproves the universal statement.

Worked examples

Try itClaim: Every prime number is odd.Show answer

2 is prime and even, so the claim is false.

Deductive Reasoning

Objective: Draw a justified conclusion from known facts.

Deductive reasoning applies definitions, postulates, or established theorems to premises. A valid argument guarantees its conclusion when its premises are true.

You finished the reading!

Lock it in with a few practice questions, then move on to the next lesson.

Practice Next lesson

Next lessonConditional Statements