Conjectures & Counterexamples

Front

A concluding statement reached using inductive reasoning is called a _______

Back

conjecture

Front

To fully disprove a conjecture, one needs to find only ONE counterexample.

Back

True

Front

Back

x = -2

Front

What is the basis for inductive reasoning?

Back

Observed patterns

Front

For a conjecture to be true, it must be true...

Back

in all cases.

Front

Counterexample for: If an animal is furry, then it is a hamster. Options: goldfish, frog, elephant, cat

Back

cat

Front

Counterexample for: "If it is a fraction, then it is a number between zero and one." Options: 2/3, 4/5, 1/2, 3/2

Back

3/2

Front

Which statement is a conjecture based on observed patterns?

• All even numbers are divisible by 2.
• Every prime number greater than 2 is odd.
• If a number ends in 0, it is divisible by 5.
• The sum of two odd numbers is always even.

Back

The sum of two odd numbers is always even.

Front

Counterexample to: 'If a shape has four sides, then it is a square'. Options: Rectangle, Triangle, Pentagon, Circle.

Back

Rectangle

Front

Used to prove that a conjecture is false.

Back

Counterexample