2.1 Inductive reasoning, conjectures, and counterexamples

Front

What is a conjecture?

Back

A statement believed to be true based on observations.

Front

Make a conjecture about the next item in the sequence: –2, 4, –8, 16, –32, ...

Back

Multiply the previous number by -2.

Front

Which number is a counterexample to the statement: 'All numbers that are divisible by 2 are divisible by 4'?

Back

42.

Front

What is a valid counterexample for the statement: 'If an animal is a panther, then it lives in the forest.'?

Back

It lives in a zoo.

Front

What are the next two numbers in this pattern: 12, 17, 22, 27, ___, ___?

Back

32, 37.

Front

What is inductive reasoning?

Back

A method of reasoning in which a general rule or conclusion is inferred from specific cases.

Front

What is a counterexample?

Back

An example that disproves a conjecture or statement.

Front

Provide an example of a conjecture.

Back

If it rains, then the ground will be wet.

Front

What is the difference between a conjecture and a theorem?

Back

A conjecture is a statement believed to be true, while a theorem is a statement that has been proven to be true.

Front

How can you prove a conjecture false?

Back

By providing a counterexample.