G.1 Counterexamples

Determine the truth value of the following statement. If the statement is false, give a counterexample.

The product of two even numbers is even.

• false: 8 x 4 = 32

• false; 7 x 6 = 42

• false; 3 x 10 = 30

• true

Which of the following best describes a counterexample to the statement?

Two lines in a plane intersect in exactly one point.

• coplanar lines

• parallel lines

• intersecting lines

• perpendicular lines

Let p= “n is an integer and n² is divisible by 4”

Let q= “n is divisible by 4”

p → q means “If n is an integer and n² is divisible by 4, then n is divisible by 4.”

What is a counterexample to p → q?

• 4

• 6

• 8

• 10

Provide a counterexample for the following:

If a number is an integer, then it is odd.

• 0

• 1

• ^½

• 3

Provide a counterexample to the statement:

All parallelograms have four right angles.

• square

• rectangle

• rhombus

• trapezoid

Take the following conditional. If true select true, if false pick the counter example. 
"If a number is divisible by 3, then it is divisible by 6."

• True
• 9
• 18
• 36

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

If it is a line, then it has a positive slope. What is an appropriate counterexample?

• y = -4x
• y = 6x
• y = 1/5x + 5
• y = 2x - 6

Tags

CCSS.HSA.REI.D.10

CCSS.HSS.ID.C.7

If it is an angle, then it is acute. What is an appropriate counterexample?

• 70⁰
• 45⁰
• 120⁰
• True. There is no counterexample.

Tags

CCSS.4.G.A.1

CCSS.4.G.A.2

CCSS.4.MD.C.5

If a three-dimensional solid has a circular base, then it is a cone. What is an appropriate counterexample?

• prism
• pyramid
• cube
• cylinder

Tags

CCSS.HSG.GMD.A.1