Inductive Reasoning and Counterexamples

Front

What is a counterexample?

Back

A specific case that shows a conjecture is false.

Front

What does inductive reasoning involve?

Back

Testing and observing patterns to make conjectures.

Front

What is the main difference between inductive and deductive reasoning?

Back

Inductive reasoning makes generalizations based on specific observations, while deductive reasoning applies general principles to specific cases.

Front

What is a conjecture?

Back

A statement or proposition that is believed to be true but has not been proven.

Front

How can you prove a conjecture is false?

Back

By providing a counterexample.

Front

If you observe that the sun rises in the east every day, what conjecture can you make?

Back

The sun will rise in the east tomorrow.

Front

What is the first step in using inductive reasoning?

Back

Making observations.

Front

What type of reasoning is used when making predictions based on patterns?

Back

Inductive reasoning.

Front

What is an example of a counterexample?

Back

If a conjecture states that all birds can fly, a penguin is a counterexample.

Front

What is the conclusion drawn from the observation: 'Every time I water my plants, they grow'?

Back

Watering plants helps them grow.