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- 1. Multiple Choice
A concluding statement reached using inductive reasoning is called a _______
compound statement
conjecture
condition
counterexample
- 2. Multiple Choice
Conjectures, like theorems, have been proven to be true.
True
False
- 3. Multiple Choice
For any right triangle, the sum of the squares of the legs is equal to the square of the hypothesis. This is an example of a conjecture.
True
False
- 4. Multiple Choice
No number of examples or cases can fully prove a conjecture.
True
False
- 5. Multiple Choice
A counterexample is an example that proves a conjecture to be true.
True
False
- 6. Multiple Choice
To fully disprove a conjecture, one needs to find only ONE counterexample.
True
False
- 7. Multiple Choice
Which of the following is a counterexample to the following conjecture? If , then x = 2
x = 4
x = -2
x = 2
x = -4
- 8. Multiple Choice
Which number is a counterexample to the following statement?
For all numbers a, 2a + 7a = 6
a = 0
a = 5
a = 1
- 9. Multiple Choice
Which numbers are not counterexamples for the following statement?
For any numbers a and b,a = 8, b = 4
a = 10, b = 5
a = 6, b = 3
a = 4, b = 2
- 10. Multiple Choice
Which answer would be a counterexample to the following biconditional?
"Greg is a swimmer if and only if he is an athlete."
Greg is an athlete and a basketball player.
Greg is a swimmer.
Greg is not an athlete
There is no counterexample.
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