{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw4cs - 1 Is this a directed graph 2 Is this graph...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
CSE 20: Discrete Mathematics Fall 2010 Problem Set 4 Instructor: Daniele Micciancio Due on: Wed. Nov 3, 2010 Problem 1 (6 points) Let A, B and C be subsets of U . Prove or disprove each of the following statements using Venn diagrams: 1. ( A \ B ) \ C = A \ ( B C ) 2. ( A \ C ) ( B \ C ) and ( A \ B ) are disjoint 3. ( A B ) C = A ( B C ) Problem 2 (5 points) Let A = { 1 , 3 } , B = { 5 , 6 } and C = { 1 , 3 , 5 , 7 , 9 } . List the elements for each of the following sets: 1. ( A B ) C 2. ( A × B ) A 3. ∅ × ∅ 4. { x C | ( x + 1) A B } 5. ( C \ ( A B )) 2 Problem 3 (8 points) Let A and B be subsets of a universal set U . Use the definition of the set operations (as given in class an in section 2.2 of the textbook) and the rules of logic to prove the following identity: ( A B ) ( A 0 B 0 ) = ( A B 0 ) ( A B 0 ) 0 Problem 4 (6 points) [Problem 2.1(9) from the textbook] Think of the internet as one big graph, where each page is a vertex and each link is an edge. Answer the following questions, and provide a brief (one line) explatation:
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1. Is this a directed graph? 2. Is this graph connected? 3. Is this graph complete? 4. In this graph simple? 5. For a given webpage p, what does the outdegree of p represent? 6. For a given webpage p, what does the indegree of p represent? Problem 5 (6 points) [Problem 2.1(13) from the textbook] Using as few groups as possible, put the words “fish”, “sit”, “stay”, “play”, “diet”, “tree”, “duck”, “dog”, and “hen” into groups such that none of the words in a group have any letters in common. Use a graph model and graph coloring. Justify your answer: explain why your grouping uses the fewest groups as possible....
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern