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10 questions
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 n^{2 }is divisible by 4”
Let q= “n is divisible by 4”
p → q means “If n is an integer and n^{2 }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
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