Conjectures and Counterexamples

Front

A concluding statement reached using inductive reasoning is called a _______

Back

conjecture

Front

Complete the conjecture. The sum of two negative numbers is ___________.

Back

negative

Front

What is the next term in the sequence? 1, 1, 2, 3, 5, 8, 13, ...

Back

21

Front

How many squares are in Figure 4?

Back

11

Front

To fully disprove a conjecture, one needs to find only ONE counterexample. True or False?

Back

True

Front

What is a conjecture?

Back

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

Front

What is a counterexample?

Back

A counterexample is an example that disproves a conjecture.

Front

If a conjecture states that all birds can fly, what would be a counterexample?

Back

An ostrich is a counterexample because it is a bird that cannot fly.

Front

What is the Fibonacci sequence?

Back

A sequence where each number is the sum of the two preceding ones, starting from 0 and 1.

Front

What is the importance of counterexamples in mathematics?

Back

Counterexamples are crucial for testing the validity of conjectures and statements.