Geo 2.4-2.5 Flashcard Part 1

Front

What is a counterexample?

Back

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

Front

What is a conjecture?

Back

A conjecture is a statement that is neither proven true nor false based on observations.

Front

What does deductive reasoning mean?

Back

Deductive reasoning involves drawing conclusions from situations based on facts and definitions.

Front

What is inductive reasoning?

Back

Inductive reasoning is the type of reasoning where conclusions are made based on observations and patterns.

Front

What is the relationship between bears and kidneys based on deductive reasoning?

Back

All bears are mammals, all mammals have kidneys; therefore, all bears have kidneys.

Front

What is the difference between inductive and deductive reasoning?

Back

Inductive reasoning makes generalizations based on specific observations, while deductive reasoning draws specific conclusions from general principles.

Front

Provide an example of a conjecture.

Back

"All swans are white" is a conjecture until proven otherwise.

Front

What is the role of a counterexample in mathematics?

Back

A counterexample is used to show that a general statement is false.

Front

How can you identify deductive reasoning in an argument?

Back

Look for arguments that start with general statements and lead to a specific conclusion.

Front

What is an example of inductive reasoning?

Back

If you observe that the sun rises in the east every day, you might conclude that the sun always rises in the east.