conjectures and counterexamples

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, showing that it is not universally true.

Front

How many counterexamples are needed to disprove a conjecture?

Back

Only one counterexample is needed to disprove a conjecture.

Front

If all squares are rectangles, is a square a counterexample to the conjecture 'not all rectangles are squares'?

Back

No, a square is not a counterexample; it supports the conjecture.

Front

What does it mean if a conjecture is true?

Back

If a conjecture is true, it means that it holds for all cases or examples considered.

Front

Provide an example of a conjecture related to even numbers.

Back

All even numbers are divisible by 2.

Front

What is the relationship between conjectures and proofs?

Back

A conjecture can be proven true or false through logical reasoning and evidence.

Front

Is the statement 'If it rains, then the ground is wet' a conjecture?

Back

Yes, it is a conjecture that can be tested and proven.

Tags

CCSS.6.SP.A.3

Front

What is the importance of counterexamples in mathematics?

Back

Counterexamples are crucial for testing the validity of conjectures and ensuring that statements are accurate.

Front

Can a conjecture be proven true for some cases but false for others?

Back

Yes, a conjecture can be true for some cases and false for others, which is why counterexamples are important.