Conjectures

Conjectures, like theorems, have been proven to be true.

• True

• False

No number of examples or cases can fully prove a conjecture.

• True

• False

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.6.EE.B.6

CCSS.6.EE.B.5

CCSS.6.EE.A.2

CCSS.6.EE.B.8

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

Which of the following conjectures is false?

• The product of two even numbers is even.
• The sum of two even numbers is even.
• The product of two odd numbers is odd.
• The sum of two odd numbers is odd.

Tags

CCSS.6.EE.B.6

Complete the conjecture.
The sum of two negative numbers is ___________.

• positive
• negative
• odd
• even

Tags

CCSS.7.EE.A.1

Which is a counterexample of: If a four sided shape has two sides the same length, then it must be a rectangle.

• quadrilateral
• rectangle
• square
• triangle

Tags

CCSS.4.G.A.2