2.1 Patterns and Inductive Reasoning

Front

What is a counterexample?

Back

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

Front

What does it mean for a number to be divisible by another number?

Back

A number A is divisible by a number B if there exists an integer C such that A = B * C.

Front

Provide an example of a number that is divisible by 2 but not by 4.

Back

An example is 2, since 2 is divisible by 2 but not by 4.

Front

What is a conjecture in mathematics?

Back

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

Front

What is the sum of two even numbers?

Back

The sum of two even numbers is always even.

Front

What is the product of two odd numbers?

Back

The product of two odd numbers is always odd.

Front

What is a linear pair of angles?

Back

A linear pair of angles are two adjacent angles whose non-common sides form a straight line.

Front

Back

They are supplementary angles.

Front

What is an example of a false conjecture?

Back

The conjecture 'The sum of two odd numbers is even' is false; it is actually odd.

Front

What is inductive reasoning?

Back

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