28 Dec MAT2051 Discrete Mathematics

MAT2051 Discrete Mathematics

Unit 2 Quiz

Question 1 What is a set?

Answers:

a. An unordered collection of objects.

b. An ordered collection of objects.

c. The study of reasoning.

d. A partition of numbers.

Question 2 What is the cardinality of the set X = {1, 5, 3, 8, 10}?

Answers:

a. 5.

b. 1.

c. 10.

d. 27.

Question 3 What value replaces ? in the following truth table?

Answers:

a. 0.

b. 1.

c. Cannot solve with the given information.

d. Can be either 0 or 1.

Question 4 Let:

P: Jerry receives a scholarship.

Q: Jerry goes to college.

Assume the statement P → Q is true.

If Jerry does not go to college, did he receive his scholarship?

Answers:

a. Yes, because the converse of the statement is true.

b. No, because the contrapositive of the statement is true.

c. There is not enough information.

d. Can be either.

Question 5 What is deductive reasoning?

Answers:

a. A hypothesis together with a conclusion.

b. Valid arguments of a hypothesis.

c. The process of drawing a conclusion from a sequence of propositions.

d. A simplification of the rules of inference.

MAT2051 Discrete Mathematics

Unit 4 Quiz

Question 1 How many different eight-bit strings begin with 100?

Answers:

a. 4.

b. 32.

c. 64.

d. 16.

Question 2 How many strings can be formed using the letters in the word router (that is, R-O-U-T-E-R)?

Answers:

a. 6!/2!

b. C(6, 1).

c. (6 1)!

d. C(1, 6).

Question 3 There are 100 processors, 30 of which are defective. If you select 20 microprocessors from these 100 microprocessors, what is the probability that you select no defective processors?

Answers:

a. C(100, 10)/C(30, 20).

b. C(100, 20).

c. C(100, 20)/C(70, 20).

d. C(70, 20)/C(100, 20).

Question 4 What is the probability of drawing a queen from a standard deck of cards?

Answers:

a. 2/52.

b. 10%.

c. 8/52.

d. 4/52.

Question 5 Assume the probability of having a boy or a girl is the same. If a family has five children, what is the probability that they are all boys?

Selected Answer:

a. 1/32.

b. 1/16.

c. 1/2 + 1/2 + 1/2 + 1/2 + 1/2.

d. 1/2.

MAT2051 Discrete Mathematics

Unit 6 Quiz

• Question 1 How many times does the computer print the string “Hello”?

i = 2

while (i < 4) { print ("Hello") i = i + 1}: Answers: a. 1. b. 2. c. 3. d. 4. • Question 2 Which of the following is O(n)? Answers: a. 3n + 1. b. n * log(n). c. n * n + n. d. None of the above. • Question 3 If each of the following describes the run time of an algorithm, which of the following could have the longest run time? Answers: a. O(nlog(n)). b. O(n!). c. O(n/2). d. O(n * n). • Question 4 What does the following algorithm return? f(n){ if (n< 2) return 1 else return f(n - 1) * n: Answers: a. n! b. The maximum divisor of n. c. (n - 1)! d. n 2. • Question 5 Given that S_n denotes the number of n-bit strings that do not contain the pattern 00, what are the initial conditions? Answers: a. S_1 = 2, S_2 =3. b. S_1 = 1, S_2 =2. c. S_1 = 0, S_2 =2. d. None of the above. MAT2051 Discrete Mathematics Unit 8 Quiz • Question 1 Is a graph a tree? Is a tree a graph? Answers: a. Yes, Yes. b. No, Yes. c. Yes, No. d. No, No. • Question 2 Given a graph with n vertices, what is the minimum number of edges needed to make the graph connected? Answers: a. n. b. n - 1. c. n * n. d. n log n. • Question 3 Given the graph below, what type of path is path (A, D, E, C, B)? Answers: a. Simple Path. b. Cycle. c. Simple cycle. d. None of the above. • Question 4 Given the graph below, which of the following is a Hamiltonian cycle? Answers: a. (A, D, B). b. (A, D, B, C, E, D, A). c. (B, C, E, D, A, B). d. (C, E, D, A, C). • Question 5 Given the graph below, what is the total weight of the shortest weighted path from A to E: Answers: a. 8. b. 5. c. 4. d. 3. MAT2051 Discrete Mathematics Unit 10 Quiz Question 1 Given an unordered list of n numbers, what algorithm would you use to sort it, and what is the worst-case runtime of the algorithm? Answers: a. Tournament sort, O(n log n). b. Tournament sort, O(n). c. Prim's Algorithm, O(n log n). d. Prim's Algorithm, O(n * n). Question 2 Given a graph with n vertices, what is the minimum number of edges needed such that the graph is connected? Answers: a. n. b. n – 1. c. n * n. d. n log n. Question 3 Which is a minimal spanning tree of the following graph: Graph A-E.[D] Answers: a. A-B-D-E-C. b. A-D-E-C-B. c. A-B-D. d. There is no minimal spanning tree. Question 4 How many six-bit strings begin with 100? Answers: a. 4. b. 8. c. 32. d. 16. Question 5 If you select 5 microprocessors from 100 microprocessors, where 30 of the 100 are defective, what is the probability that you select no defective processors? Answers: a. C(100, 10)/C(30, 5). b. C(70, 5)/C(100, 5). c. C(100, 5). d. C(100, 5)/C(70, 5).