Search & Filtering
Let R be the relation on X = {1,2,3} defined by (x,y) ∈ R if x<y
- List the elements of R (ordered pair)
- Find the range of R
- Find the domain of R
- Draw the Diagraph of R below
- Identify the properties of R (kind of graph)
Suppose that 53 of the 55 Information Technology students of University of Northern Philippines are taking atleast one of the mathematics subjects Mathematics in the Modern World, Discrete Mathematics, and Data management. Also suppose that: 24 taking Mathematics in the Modern World, 26 taking Discrete Mathematics, and 20 taking Data Management, 5 taking Mathematics in the Modern World and Discrete Mathematics, 7 taking Mathematics in the Modern World and Data Management, 8 taking Discrete Mathematics and Data Management.
E. How many students were taking Data Management and Discrete Mathematics but not Mathematics in the Modern World?
F. How many students did not take any of the mathematics subjects mentioned in the problem?
Suppose that 53 of the 55 Information Technology students of University of Northern Philippines are taking atleast one of the mathematics subjects Mathematics in the Modern World, Discrete Mathematics, and Data management. Also suppose that: 24 taking Mathematics in the Modern World, 26 taking Discrete Mathematics, and 20 taking Data Management, 5 taking Mathematics in the Modern World and Discrete Mathematics, 7 taking Mathematics in the Modern World and Data Management, 8 taking Discrete Mathematics and Data Management.
A. Fill in the correct number of students in each of the eight regions of the Venn Diagram.
B. Find the number of students who are taking all three mathematics subjects.
C. Determine the number of students who are not taking any of the three mathematics subjects?
D. How many students were taking Mathematics in the Modern World as their only mathematics subject?
1. Let p, q, and r be the propositions
p: You have the flu.
q: You miss the final examination.
r: You pass the course.
Express each of these propositions as an English sentence.
a) p → q
b) ¬q ↔ r
c) q →¬ r
d) p ∨ q ∨ r
e) (p → ¬r) ∨ (q → ¬r)
Given the following propositions.
Let A : Mohammad is Malaysian.
Let B : Lucy is Italian.
Formalize the following sentences using propositional logic.
i. Lucy isn’t Italian. (1 mark)
ii. If Mohammad is Italian then Mohammad is not Malaysian. (1 mark)
iii. Muhammad is Malaysian or if Mohammad isn’t Malaysian then Lucy is Italian.
(2 marks)
iv. Either Mohammad is Malaysian and Lucy is Italian, or neither Mohammad is not
Malaysian nor is Lucy Italian.
Let R = {(0,1),(0,2),(1,1,),(1,3),(2,2),(3,0)} be a relation defined on
A = {0,1,2,3}.Find the zero-one matrix of transitive closure of R.
Prove that there is a positive multiple of 3333 which is entirely made of 0s and 1s. (For example: 110000011; note that we don’t need to find the number. We just need to prove that there exists such a number)
Let p, q, and r be the propositions
p: You get an A on the final exam.
q: You do every exercise in this book.
r: You get an A in this class.
Write these propositions using p, q, and r and logical connectives (including negations).
1. You get an A on the final, you do every exercise in this book, and you get an A in this class.
2. To get an A in this class, it is necessary for you to get an A on the final.
3. You get an A on the final, but you don’t do every exercise in this book; nevertheless, you get an A in this class.
4. Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class.
Let p, q, and r be the propositions
p: You have the flu.
q: You miss the final examination.
r: You pass the course.
Express each of these propositions as an English sentence.
p → q
¬q ↔ r
q →¬ r
p ∨ q ∨ r
(p → ¬r) ∨ (q → ¬r)
Let p, q, and r be the propositions
p: You have the flu.
q: You miss the final examination.
r: You pass the course.
Express each of these propositions as an English sentence.
p → q
