conjectures and counterexamples

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

What is a counterexample?

Back

A counterexample is an example that disproves a conjecture or statement, showing that it is not universally true.

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

How do you determine if a conjecture is true?

Back

To determine if a conjecture is true, you must prove it through logical reasoning or find a counterexample.

Front

What is the importance of counterexamples in mathematics?

Back

Counterexamples are crucial in mathematics as they help to identify the limitations of conjectures and refine theories.

Front

If a four-sided shape has two sides the same length, then it must be a rectangle. What is a counterexample?

Back

A square is a counterexample because it has two sides of the same length but is not a rectangle.

Front

What is the next number in the sequence: 1, -1, 2, -2, 3, ___?

Back

-3

Front

How many squares are in Figure 4 if the answer is 11?

Back

There are 11 squares in Figure 4.

Front

What is the next number in the pattern: 5, 7, 9, ___?

Back

11

Front

What does it mean for a conjecture to be proven?

Back

A conjecture is proven when a logical argument or mathematical proof demonstrates its truth in all cases.