# Logic in Mathematics: Help and Review Chapter Exam

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### Page 1

#### Question 1 1. Triangles have 180 degrees in total, and squares are two triangles put together. What can you say about the total degrees of a square?

#### Question 2 2. What is the conclusion in the following statement? 'If p and q are odd integers, then pq is odd.'

#### Question 3 3. Which of the following occurs with a direct proof?

#### Question 4 4. Which of the following connectors is the logical disjunction?

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Question 5
5.
Which is a correct logical disjunction formed with the following phrases?

Algebra is easy.

Geometry is a breeze.

### Page 2

#### Question 6 6. Which of the following is a conditional statement?

#### Question 7 7. In a 2-column proof, what goes in the column on the left?

#### Question 8 8. Which of the following connectors is the logical conjunction?

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Question 9
9.
p: The pond is not frozen over.

q: The fish are not jumping.

For the combination p AND (NOT q), for which truth values of p and q is the combination true?

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Question 10
10.
Which type of logical fallacy is illustrated below?

Everyone in the class agrees that if x = 2 and y = 2, then x must equal y.

### Page 3

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Question 11
11.
Which is a correct logical conjunction formed with the following phrases?

Drew likes roses.

Drew loves lilies.

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Question 12
12.
What kind of logic is presented below?

Your dog loves rock and roll music because my dog loves rock and roll music.

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Question 13
13.
Which type of logical fallacy is illustrated below?

This chocolate pie must be bad because nobody is taking it.

#### Question 14 14. What is an example of a logical fallacy?

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Question 15
15.
p: The dog rolls over on command.

q: The dog gets a treat.

For the combination p AND q, for which truth values of p and q is the combination true?

### Page 4

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Question 16
16.
Provide a counterexample for the statement below.

All prime numbers are odd.

#### Question 17 17. All of the following statements could be proven with a direct proof EXCEPT:

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Question 18
18.
If the following two propositions are true, which is a true statement?

Theresa loves dogs.

Spot is a dog.

#### Question 19 19. Which of the following is a conditional statement?

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Question 20
20.
Which type of logical fallacy is illustrated in the example below?

I will get an A in math class because I spent many sleepless nights studying.

### Page 5

#### Question 21 21. Which statement is an example of circular reasoning?

#### Question 22 22. All of the following are recommended steps when completing geometry proofs EXCEPT:

#### Question 23 23. What is the hypothesis in the following statement? 'If p is an even integer and q is an odd integer, then p + q is an odd integer.'

#### Question 24 24. If x = 1 and y = 2, what can be said about z if z = xy?

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Question 25
25.
Which logical fallacy is shown below?

Statement 1: If the deer has a red nose, then it is a reindeer.

Statement 2: If it is a reindeer, then the deer has a red nose.

### Page 6

#### Question 26 26. What does the statement, 'We will go get ice cream if and only if you clean your room' mean?

#### Question 27 27. A statement can be determined to be which of the following through a direct proof?

#### Question 28 28. What kind of reasoning uses two unrelated events to prove a point?

####
Question 29
29.
Which of the following is the contrapositive of the following statement.

If a quadrilateral has four sides, then it is a square.

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Question 30
30.
An example of which topic discussed in this lesson is shown below?

Statement 1: All quadrilaterals are parallelogramps.

Statement 2: Kite

#### Logic in Mathematics: Help and Review Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!