INC Counterexamples and Conjectures

Front

What is a counterexample?

Back

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

Front

If it is an angle, then it is acute. What is a counterexample?

Back

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

Front

True or False: A counterexample proves a conjecture to be true.

Back

False. A counterexample disproves a conjecture.

Front

True or False: To disprove a conjecture, only one counterexample is needed.

Back

True. One counterexample is sufficient to disprove a conjecture.

Front

What is the next term in the sequence: 1, 3, 7, 15, 31, ___?

Back

63 is the next term.

Front

What is the next term in the sequence: 1, 3, 7, 15, 31, 63, ___?

Back

127 is the next term.

Front

If an animal is furry, then it is a hamster. What is a counterexample?

Back

A cat is a counterexample because it is furry but not a hamster.

Front

Define conjecture in mathematics.

Back

A conjecture is a statement that is believed to be true but has not yet been proven.

Front

What is the purpose of finding a counterexample?

Back

The purpose is to show that a conjecture is false.

Front

What does it mean if a conjecture is true?

Back

It means that there are no counterexamples that disprove it.