Conjectures & Counterexamples

Front

What must be true for a conjecture to be considered true?

Back

A conjecture must be true in all cases.

Front

What is a concluding statement reached using inductive reasoning called?

Back

A concluding statement reached using inductive reasoning is called a conjecture.

Front

What is used to prove that a conjecture is false?

Back

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

Front

Provide a counterexample to the claim: 'If two angles are supplementary, then they are not congruent.'

Back

Front

To fully disprove a conjecture, how many counterexamples are needed?

Back

Only one counterexample is needed to fully disprove a conjecture.

Front

Define 'conjecture' in the context of 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 a counterexample?

Back

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

Front

What is the difference between inductive reasoning and deductive reasoning?

Back

Inductive reasoning involves making generalizations based on specific observations, while deductive reasoning involves drawing specific conclusions from general principles.

Front

What is the role of a counterexample in mathematical proofs?

Back

A counterexample demonstrates that a conjecture is false by providing a specific case where the conjecture does not hold.

Front

Can a conjecture be true in some cases and false in others?

Back

Yes, a conjecture can be true in some cases and false in others, but to be considered true, it must hold in all cases.