Lesson 2.1 Inductive Reasoning and Conjectures

Front

What is inductive reasoning?

Back

Inductive reasoning is a method of reasoning in which a general conclusion is drawn from specific examples or patterns.

Front

What is a conjecture?

Back

A conjecture is a statement or proposition that is believed to be true based on observations but has not yet been proven.

Front

How can you prove a conjecture is false?

Back

By providing a counterexample.

Front

What is a counterexample?

Back

A counterexample is an example that disproves a conjecture or statement.

Front

If all numbers that are divisible by 2 are divisible by 4, what is a counterexample?

Back

42 is a counterexample because it is divisible by 2 but not by 4.

Front

What is the significance of finding a counterexample?

Back

Finding a counterexample is significant because it can fully disprove a conjecture.

Front

True or False: To fully disprove a conjecture, one needs to find only ONE counterexample.

Back

True.

Front

What is an example of a counterexample for the statement: If it is an angle, then it is acute?

Back

120° is a counterexample because it is an angle but not acute.

Front

What is a rhombus in relation to quadrilaterals?

Back

A rhombus is a quadrilateral with four equal sides but is not necessarily a square.

Front

What is the difference between a conjecture and a theorem?

Back

A conjecture is an unproven statement, while a theorem is a statement that has been proven based on previously established statements.