1.4 Inductive Reasoning, Conjectures & Counterexamples

Front

What is inductive reasoning?

Back

Inductive reasoning is a method of reasoning in which a general conclusion is drawn from specific examples or patterns.

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.

Front

If all angles are acute, what is a counterexample?

Back

120° is a counterexample because it is not acute.

Front

What is the next number in the pattern: 2, 4, 8, 14, 22, ...?

Back

The next three numbers are 32, 44, 60.

Front

How do you find the midpoint between two points?

Back

To find the midpoint, average the x-coordinates and the y-coordinates of the two points.

Front

What is the midpoint between (3, -1) and (8, -7)?

Back

The midpoint is (5.5, -4).

Front

Which number is a counterexample to: All numbers divisible by 2 are divisible by 4?

Back

42 is a counterexample because it is divisible by 2 but not by 4.

Front

What is the purpose of a counterexample?

Back

A counterexample is used to prove that a conjecture is false.

Front

What is the first step in inductive reasoning?

Back

The first step is to observe specific examples or patterns.