Games for Educators

Discuss the role that counterexamples play in showing that a statement is false.

Simple Statements With Counterexamples

• All trucks have four wheels.- Large trucks often have 6, 10 or more wheels.
• All rectangles are squares.- Rectangles need not have all their sides the same length.
• All birds can fly.- Ostriches, emus, and kiwis are birds that cannot fly.
• The moon is only visible at night.- The moon is often visible during the day.
• All shapes have straight sides.- A circle does not have a straight side.
• All playgrounds have swing sets.- Some playgrounds don’t have swing sets.
• All rooms have chairs. Bedrooms and bathrooms often don’t have a chair.

If – Then Statements With Counterexamples

• If today is Monday, then it is a school day.- Some Mondays are holidays or occur during the summer.
• If I don’t eat for 3 hours, then I’m hungry.- Most people sleep more than 3 hours and are not hungry.
• If a person is taller, then they are older.- Children often grow up to be taller than their parents.
• If the sun is shining, it is a warm day.- Winter days can be sunny and cold.
• If someone is late, something bad must have happened to them.- Sometimes people are late through carelessness or reasons beyond their control (traffic, bad weather, car trouble).