MAT2051 Unit 2 Quiz (October 2019)

MAT 2051 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.

Question 6 Assume that ~, v, and ^ are the NOT, OR, and AND symbols, respectively. Use a truth table to determine if the following Boolean equation ~x1 v (x2 ^ x1):

Answers:

a. Is functionally identical to an AND gate.

b. Is functionally identical to an OR gate.

c. Is not like an AND or an OR gate.

d. Is a NOT gate.

Question 7 The function f(x) = x + 3 is best described as:

Onto the reals.

Answers:

a. One-to-one with the reals.

b. Onto the reals.

c. Is a bijection with the reals.

d. Is neither one-to-one nor onto.

Question 8 Given a hash function h(n) = n mod 5, what would a computer’s memory cells look like if we were to input values 2, 10, and 14?

Unit 2 Quiz, Question 8. The answers are tables, they are noted here in order (matched with the letter.)[D]

Answers:

a. a.

b. b.

c. c.

d. d.

Question 9 How many strings of length 2 can be created from the set X = {a, b, c} without replacement (without replacement simply means that you cannot use the same element more than once).

Answers:

a. 6.

b. 8.

c. 24.

d. 12.

e. 16.

Question 10 Represent the following database as n-ary tuples:

Database Table.[D]

Answers:

a. {(Joe Smith, Smith21, 1),(Jane Doe, Jdoe1, 1), (Tim Thomas, TimT, 5)}.

b. {(Joe Smith, Jane Doe, Tim Thomas), (Smith21, Jdoe1, TimT), (1, 1, 5)}.

c. {(Joe, Smith, Smith21, 1), (Jane, Doe, Jdoe1, 1), (Tim, Thomas, TimT, 5)}.

d. {(Joe, Smith, Jane, Doe, Tim, Thomas), (Smith21, Jdoe1, TimT), (1, 1, 5)}