Problem 1I’m sure you have all encountered the concept of a set, such as {1,2,5} or the set of all positive rational numbers. In each of the four parts of Problem
Problem 1I’m sure you have all encountered the concept of a set, such as {1,2,5} or
the set of all positive rational numbers. In each of the four parts of Problem
1, in order that the problem be completely defined, it is necessary to specify
a universe of discourse, which is a set to which the statement in the
Need assignment help for this question?
If you need assistance with writing your essay, we are ready to help you!
OUR PROCESS
Order
Payment
Writing
Delivery
Why Choose Us: Cost-efficiency, Plagiarism free, Money Back Guarantee, On-time Delivery, Total Сonfidentiality, 24/7 Support, 100% originality
problem applies.
The universes of discourse for the four parts are:
(a) The set of all integers
(b) The set of all students enrolled at UMUC
(c) The set of all integers
(d) The set of students in this section of CMSC 150
The remaining problems do not require clarification.
Which of the following sentences are logical statements? (20 points, 4 parts- 5 points
each)
a. If x even divides y, then x is a factor of y
b. If John does well in discrete math, then he will be an excellent programmer
c. 2 is the only even prime number
d. He is the best student in the class
Construct the truth tables for the following propositions: (20 points, 4 parts-5 points each)
a. (p ∧ ¬ p) ∧ q
b. (p ∨ q) ∧ (q ∨ ¬ p)
c. p ∧ (q ∨ ¬ r)
d. (p ∧ q) ∨ (p ∧ r)
Refer to the propositions in problem 2. For each of them, indicate whether it is a
tautology, a contradiction or neither. (20 points, 4 parts – 5 points each)
Use truth tables to determine whether the following is valid argument: (20 points)
p → q
q → p
∴ p ∨ q
Use truth tables to determine whether each of the following pairs of propositions are
logically equivalent. (20 points, 2 parts – 10 points each)
a. (p ∨ q) ∧ ¬ q
¬ q ∧ (q ∨ p)
b. (¬ (p ∧ q)) ∨ q
(¬ p ∧ ¬ q) ∨ q