# 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 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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