Conjectures and Counterexamples (Grade 10)
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Conjectures and Counterexamples
1.
A concluding statement reached using inductive reasoning is called a
- compound statement.
- conjecture.
- condition.
- counterexample.
2.
Conjectures, like theorems, have been proven to be true.
- True
- False
3.
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.
No number of examples or cases can fully prove a conjecture.
- True
- False
5.
A counterexample is an example that proves a conjecture to be true.
- True
- False
6.
To fully disprove a conjecture, one needs to find only ONE counterexample.
- True
- False
7.
Which of the following is a counterexample to the following conjecture? If [math]x^2=4[/math], then [math]x=2[/math]
- x = 4
- x = -2
- x = 2
- x = -4
8.
Which number is a counterexample for the following statement?
For all numbers a, 2a + 5 < 17.
For all numbers a, 2a + 5 < 17.
- a = 6
- a = 0
- a = 5
- a = 1
9.
Which numbers are not counterexamples for the following statement?
For any numbers a and b, a/b = a - b
For any numbers a and b, a/b = a - b
- a = 8, b = 4
- a = 10, b = 5
- a = 6, b = 3
- a = 4, b = 2
10.
Which answer would be a counterexample to the following biconditional?
"Greg is a swimmer if and only if he is an athlete."
"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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