Counterexamples and Conjectures

A counterexample is an example that proves a conjecture to be true.

• True

• False

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

• True

• False

Which of the following is a counterexample to the following conjecture? If  $x^2\ =\ 4$ , then x = 2

• x = 4

• x = -2

• x = 2

• x = -4

Tags

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.4

Which number is a counterexample to the following statement?
For all numbers a, 2a + 7 $\le17$  

• a = 6

• a = 0

• a = 5

• a = 1

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

Which numbers are not counterexamples for the following statement?
For any numbers a and b,  $\frac{a}{b}\ =\ a\ -\ b$  

• a = 8, b = 4

• a = 10, b = 5

• a = 6, b = 3

• a = 4, b = 2

Tags

CCSS.6.EE.A.1

A concluding statement reached using inductive reasoning is called a _______

• compound statement

• conjecture

• condition

• counterexample

Which of the following is the basis for inductive reasoning?

• definitions and accepted properties

• facts and rules

• laws of logic

• observed patterns

Tags

CCSS.4.OA.C.5

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

• in most cases.

• in all cases.

• on Thursday mornings.

• at least once.

Tags

CCSS.HSS.IC.A.1

If an animal is furry, then it is a hamster. What would be an appropriate counterexample?

• goldfish
• frog
• elephant
• cat

Tags

CCSS.HSS.CP.A.5

If it is a fraction, then it is a number between zero and one. What is an appropriate counterexample?

• 2/3
• 4/5
• 1/2
• 3/2

Tags

CCSS.6.NS.C.7A

CCSS.6.NS.C.7B