Inductive reasoning, conjectures, & counterexamples

Front

What is inductive reasoning?

Back

Inductive reasoning is a type of reasoning that involves making generalizations based on specific observations or patterns. It allows one to form conclusions that may not be universally true.

Front

Define 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 statement or proposition, showing that it is not universally true.

Front

If an angle is obtuse, what is a possible counterexample to the statement 'If an angle is obtuse, then it is 125°'?

Back

160° is a counterexample because it is obtuse but not equal to 125°.

Front

Which number serves as a counterexample to the statement 'All numbers that are evenly divisible by 2 are also evenly divisible by 4'?

Back

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

Front

What is an example of a counterexample for the statement 'If an animal is a panther, then it lives in the forest'?

Back

It lives in a zoo is a counterexample because it shows that a panther can live outside of a forest.

Front

What is a valid counterexample for the statement 'If it is an angle, then it is acute'?

Back

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

Front

What type of reasoning involves drawing conclusions from specific examples?

Back

Inductive reasoning.

Front

Provide an example of a conjecture related to even numbers.

Back

All even numbers are divisible by 2.

Front

What is the difference between inductive and deductive reasoning?

Back

Inductive reasoning makes generalizations based on specific instances, while deductive reasoning starts with general principles to reach specific conclusions.