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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1) One of the following is false; indicate by letter which one: 1) A) {4} {3, 4, 5, 6} B) 5 {3, 4, 5, 6} C) 4 {3, 4, 5, 6} D) 4 {3, 4, 5, 6}
Answer: C
Explanation: A) B) C) D)
2) Which of the following is NOT a subset of the set {p, o, 7}? 2) A) {p, o, 7} B) {o, 7} C) D) 7
Answer: D
Explanation: A) B) C) D)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
3) A combination lock on a suitcase has 5 wheels, each labeled with digits 1 to 8. How many 5-digit combination lock codes are possible if no digit can be repeated? 3)
Answer: 6,720
Explanation:
4) A test is composed of 4 multiple choice problems and 8 questions that can be answered true or false. Each multiple choice problem has 4 choices. How many different response sheets are possible if only one choice is marked for each question? 4)
Answer: (44)(28) = 65,536
Explanation:
5) How many nine-digit ZIP code numbers are possible if the first digit cannot be a four and adjacent digits cannot be the same? 5)
Answer: 99 = 387,420,489
Explanation:
6) How many different five-letter code words are possible from the first ten letters of the alphabet if the first letter cannot be a vowel and adjacent letters must be different. 6)
Answer: 45,927
Explanation:
7) Construct a truth table to determine whether or not the following implication is true: (p q) p q. 7)
Answer:
p q p q (p q) p q p q
T T T F F F F
T F T F F T F
F T T F T F F
F F F T T T T
It is true since the fourth column and the seventh column are identical.
Explanation:
8) State the converse and contrapositive of the position, "If n is an integer that is a multiple of 15, then n is an integer that is a multiple of 3 and a multiple of 5."
Answer: Converse (q p): If n is an integer that is a multiple of 3 and a multiple of 5, then n is an integer that is a multiple of 15.
Contrapositive ( q p): If n is an integer that is not a multiple of 3 and 5, then n is not a multiple of 15.
Explanation:
8)
9) Construct a truth table for the proposition and determine whether it is a contingency, a tautology, or a contradiction: ~p q. 9)
Answer:
p ~p q ~p q
T F T T
T F F F
F T T T
F T F T
Contingency
Explanation:
10) A person purchasing a new car has several options: 6 interior color choices, 5 exterior color choices, 2 choices of radios, and 5 choices of body styles. How many different cars are possible if one choice is made for each option?
Answer: (6)(5)(5)(2) = 300
Explanation:
10)
Use a Venn Diagram and the given information to determine the number of elements in the indicated region.
11) Let U = {a, l, i, t, e}, A = {l, i, t},B = {l, e}, C = {a, l, i, t, e}, and D = {a, e}. Find (C B ) A 11)
Answer: {a, i, t, e}
Explanation:
Provide an appropriate response.
12) A coin that can turn up either heads (H) or tails (T) is flipped. If a head turns up on the first toss, a spinner that can land on any of the first 7 natural numbers is spun. If a tail turns up, the coin is flipped a second time. What are the different possible outcomes?
Answer: {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (H, 7), (T, H), (T, T)}
Explanation:
12)
13) Construct a truth table for the proposition and determine whether it is a contingency, a tautology, or a contradiction: (q p) q.
Answer:
q p q p q (q p) q
T T T F F
T F T F F
F T T T T
F F F T F
Contingency
Explanation:
Use a Venn Diagram and the given information to determine the number of elements in the indicated region. 14) In a marketing survey involving 1,000 randomly chosen people, it is found that 660 use brand P, 440 use brand Q, and 220 use both brands. How many people in the survey use brand P and not brand Q?
Answer: 440
Explanation:
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Construct a truth table for the proposition. 15) p q 15) A) p q ( p q)
Answer: C
Explanation: A) B) C) D)
Let A = {6, 4, 1, {3, 0, 8}, {9}}. Determine whether the statement is true or false. 16) {3, 0, 8} A 16) A) True B) False
Answer: A
Explanation: A) B)
17) 15! 14! 17)
A) 30 B) 7 C) 14 D) 15
Answer: D
Explanation: A) B) C) D)
Construct a truth table to decide if the two statements are equivalent. 18) p q; (p q) 18)
A) True
Answer: A
Explanation: A) B)
B) False
Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let
A = {n N| n > 50}
B = {n N| n < 250}
O = {n N| n is odd}
E = {n N| n is even}
19) A' 19)
A) infinite B) finite
Answer: B
Explanation: A) B)
Construct a truth table to decide if the two statements are equivalent. 20) q p ; q p 20)
A) True
Answer: B
Explanation: A) B)
B) False
Use a Venn Diagram and the given information to determine the number of elements in the indicated region. 21) At Southern States University SSU) there are 719 students taking Finite Mathematics or Statistics. 328 are taking Finite Mathematics, 476 are taking Statistics, and 85 are taking both Finite Mathematics and Statistics. How many are taking Statistics but not Finite Mathematics? 21) A) 243 B) 158 C) 634 D) 391
Answer: D
Explanation: A) B) C) D)
Use the Venn diagram below to find the number of elements in the region.
22) n((A B) C)
A) 11 B) 15 C) 33 D) 14
Answer: B
Explanation: A) B) C) D)
Solve the problem.
22)
23) How many ways can a committee of 2 be selected from a club with 12 members? 23) A) 33 B) 66 C) 2 D) 132
Answer: B
Explanation: A) B) C) D)
Tell whether the statement is true or false.
24) 0 24)
A) True B) False
Answer: A
Explanation: A) B)
Use the addition principle for counting to solve the problem.
25) If n(A) = 5, n(B) = 11 and n(A B) = 3, what is n(A B)?
25) A) 13 B) 14 C) 11 D) 12
Answer: A
Explanation: A) B) C) D)