##### QUESTIONS

##### I. MATCHING

1. Natural Number a. Elements Common To All Sets

2. Even Number b. Have The Same Cardinal Number

3. Inductive Reasoning c. If-Then Statement

4. Deductive Reasoning d. If And Only If

5. Conditional e. Number Of Set Elements

6. Negation f. Contained in but not equal to

7. Universal Set g. Not In Set “A” Relative To Universal Set

8. Empty Set h. General To Specific Reasoning

9. Union i. Changes The Truth Value

10. Intersection j. All, Some, None

11. Complement k. And

12. Equivalent Sets l. {1, 2, 3, …}

13. Proper Subset m. Specific To General Reasoning

14. Infinite o. Meaningful Assertion Either True or False

15. Cardinal Number p. Or

16. Conjunction q. Without End

17. Disjunction r. Elements In Either Set

18. Statement s. Totality For A Given Discussion

19.Biconditional t. Divisible by two evenly

20. Quantifiers u. Cardinal Number Is Zero

##### II. MULTIPLE CHOICE

1. Patience is a virtue to the problem solving process, because it gives time to:

a. Develop a game plan for the problem resolution.

b. Fully understand the problem and what it involves.

c. Assemble various strategies that could be used to solve the problem.

d. Think about the problem.

e. All of the above.

2. Which type of reasoning progresses from specific to general?

a. Top-down b. Bottom-up c. Deductive d. Inductive e. Intuitive

3. Succeeding terms of an arithmetic progression are found by adding

a. A common difference

b. A level 2 multiple

c. A surface-level factor

d. A degree of the vertex

e. Not given

4. Succeeding terms of a geometric progression are found by multiplying by

a. A common difference

b. A common factor

c. A surface-level sum

d. The degree of the vertex

e. Not given

5. The next term of {0, 1, 4, 9, 16, 25, 36, …} is:

a. 47 b. 48 c. 49 d. 50 e. 51

6. Is set C = {10,20,30,…} infinite or finite?

a. finite b. infinite

7. Is set S = {Alabama, Alaska, …, Wisconsin, Wyoming} infinite or finite?

a. Infinite b. finite

8. List the elements of {x|x is a prime number} in roster form.

a. {3,5,7,9,…} b. {1,3,5,7,…} c. {1,2,3,5…} d. {2,3,5,7,…} e. none of these

9. List the months of the year beginning with “B” in roster notation.

a.{} b. 0 c. {} d. none of these

10. Given sets A and B: A = {0,1,2,…,100,…} ; B = {10,20,30,…} Which is true?

a. B = A b. A B c. B A d. B A e. none of these

11. If A B and B A then which of the following statements are true?

a. A B. b. B A. c. A=B d. none of these

12. If a set contains n elements, then it has _______________ subsets.

a. 2^n b. 2n c. n! d. n^2 e. none of these

13. Given U = {0,1,2,3,4,5,6,7,8,9} and A = {0,2,4,6,8}, find A’.

a. {0,2,4,6,8} b. {1,3,5,7,9} c. {0,1,2,3,4,5,6,7,8,9} d. {} e. none of these

14. Given U = {x|x is a positive integer} and A = {x|x is an integer and x100} find A’.

a. {1,2,3,…,100} b. {1,2,3,…,99}

c. {x|x is a positive integer} d. {x|x is a negative integer}

e. {x|x is an integer greater than 100}

15. What type of statement is the following? That is not the president.

a. simple b. negation c. conjunction

c. disjunction e. conditional f. biconditional

16. What type of statement is the following? Her speech was informative, but I had to leave.

a. simple b. negation c. conjunction

d. disjunction e. conditional f. biconditional

17. What type of statement is the following? She will participate orally or write an essay.

a. simple b. negation c. conjunction

d. disjunction e. conditional f. biconditional

18. What type of statement is the following? If Sherry saves the money, she can visit her friends.

a. simple b. negation c. conjunction

d. disjunction e. conditional f. biconditional

19. What type of statement is the following? The pond will freeze iff the temperature is below 32°F.

a. simple b. negation c. conjunction

d. disjunction e. conditional f. biconditional

20. What type of statement is the following? John went to the store and got some bread.

a. biconditional b. conditional c. conjunction d. disjunction e. negation

21. What type of statement is the following? Jody will stay home and study or go to the movie with Jeff.

a. biconditional b. conditional c. disjunction d. conjunction e. negation

22. Identify the following type of statement. If a student receives an A, then he is the teacher’s pet.

a. biconditional b. conditional c. conjunction d. disjunction e. negation

23. Identify the following statement type. If Kim stops for lunch and Skip brings Flip home for dinner,

then Chip won’t have to clean the kitchen until tomorrow.

a. biconditional b. conditional c. conjunction d. disjunction e. negation

24. Identify the following type of statement. I will retire early and read a book iff it is dark or noisy out.

a. biconditional b. conditional c. conjunction d. disjunction e. negation

25. Identify the following type of symbolic statement. (P ~Q) R

a. biconditional b. conditional c. conjunction d. disjunction e. negation

# III. TRUE (T) / FALSE (F)

1. Observation is rarely a useful problem-solving tool since most problems can be solved instinctively.

2. Deductive reasoning is the process of arriving at a specific conclusion based on less specific data.

3. 38 {0,2,4,6,…}

4. 10 {0,2,4,6}

5. 0{ }.

6. {Red} {x|x is a color).

7. Train {Car, Boat, Train, Plane, Bus}

8. 0.25 {x|x is a real number between 0 and 1}

9. {1,2,3,…}

10. {} { }

11. { } {0}

12. For all A, B and C, if A B and B C, then A= C.

13. Two sets whose intersection is the empty set are said to be disjoint.

14. A B is the set of elements that are members of either set A or set B or both.

15. A B is the set of elements that are members of either set A or set B or both.

16. A B = {x|x A x B}

17. (A B)’ = {x|x U but x A or x B}

18. The following is a *simple* statement: It is currently 70° outside.

19. The following is a *compound *statement: It is currently 70°, but the forecast high was 65°.

20. The following is an example of a negation: It is not raining outside.

21. ~ (P Q) = ~ P ~ Q

22. P Q is true when either P or Q is true or both are true.

23. If P is true and Q is false, then the expression P Q is true.

24. If P is true and Q is false, then the expression ~(P Q) is true.

25. A biconditional is true when both P and Q have the same truth-value.

26. A truth table with all true results exhibits a tautology.

## IV. ESSAY

1. Posted on the front door of a restaurant is the following sign:

### WINTER HOURS

Breakfast Þ served anytime

Lunch Þ 10:30 – 2:00

Dinner Þ 5:30 – 11:00

Interpret breakfast serving in light of the sign?

2. You are reading a novel and come across the following sentence: “The syzygy of Jupiter, Venus

and the moon was an impressive sight”. What do you think “syzygy” means?

3. A mother said to her baby, “oh, you are a cutie-pie?” Translate this into seven-letters.

4. Give the next value in the set of numbers: {4, 12, 20, 28, __}

5. List the next value in the set of numbers: {1/4, 1/12, 1/36, __}

6. What is the next value in the sequence: 1, 8, 27, 64, __

7. A saleswoman sells three types of computer software packages and receives $25, $15, and $5 commission for each sale

of A-package, B-package, and C-package respectively. If she sells 6 A-packages, 12 B-packages, and 9 C-packages, what

is her total monthly commission?

8. A sale conducted at a thrift shop lowers the price of an article 1¢ the first day, 2 additional cents the second day,

4 additional cents the third day, 8 additional cents the fourth day, and so on, until the article is sold or the sale ends.

Until what day of the sale must a customer wait to purchase an article originally priced at $29.95 if she is willing to

pay at most $12.00 for it?

9. A college graduate was offered a job with beginning salary of $34,500 per year with annual raises of $1,500. Give the graduates total earnings over the next 15 years under this salary schedule?

10. List all possible subsets of {0, 1, 2}.

11. A jar contains nickels, dimes, and quarters. You reach into the jar and take exactly twenty-three coins.

a. What is the minimum value of money you took?

b. What is the maximum value of money you took?

12. A jar contains pennies, nickels, dimes, and quarters. Without looking or feeling, you take three of the coins.

a. List all possible sets of three coins you might select

b. List all possible three coin total value you might select.

13. A survey of 70 hot dog lovers revealed: 43 used mustard, 31 used cheese, and 23 used relish. Sixteen used mustard and

cheese, 12 used mustard and relish, 8 used cheese and relish, while five used all three. How many used:

a. Only mustard

b. Only relish

c. Only cheese

d. Mustard and cheese but not relish

e. Mustard and relish but not cheese

f. Cheese and relish but not mustard

g. None of the three

14.Let R = Sam is awake, and S = The sun is up. Write each of the following expressions in words.

a. S ~R

b. R S

c. ~S ~R

d. ~R ~S

15. Complete the truth table for the given expression. Give only your final column as a row on the answer sheet.

P Q ~ p q

T T

T F

F T

F F

16. Complete the truth table for the given expression. Give only your final column as a row on the answer sheet.

P Q ~ ( p ~ q )

T T

T F

F T

F F

#### ANSWER SHEET

__Matching__ Multiple Choice __True (T) / False (F)__ __Essay__

1. 1. 1. 1.

2. 2. 2. 2.

3. 3. 3. 3.

4. 4. 4. 4.

5. 5. 5. 5

6. 6. 6. 6.

7. 7. 7. 7.

8. 8. 8. 8.

9. 9. 9. 9.

10. 10. 10. 10.

11. 11. 11. 11a.

12. 12. 12. 11b.

13. 13. 13. 12a.

14. 14. 14. 12b.

15. 15. 15. 13a.

16. 16. 16. 13b.

17. 17. 17. 13c.

18. 18. 18. 13d.

19. 19. 19. 13e.

20. 20. 20. 13f.

21. 21. 13g.

22. 22. 14a.

23. 23. 14b.

24. 24. 14c.

25. 25. 14d.

26. 15.

16.

. .

.