{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# HW9 - EECS 203 DISCRETE MATHEMATICS Homework 9 Due Tuesday...

This preview shows page 1. Sign up to view the full content.

EECS 203: DISCRETE MATHEMATICS Homework 9 Due Tuesday, December 4 at 4pm Put your name and discussion section number (not the meeting time) on the first page of your homework. Submit your homework to (a) CTools, as a PDF file, or (b) the drop box marked “EECS 203” in room EECS 2420. If neither (a) nor (b) is possible please turn in your homework at one of the discussion sections. 1. (9 points) If R V × V is a binary relation over V then R - 1 (the inverse) is defined as: ( x, y ) R if and only if ( y, x ) R - 1 . Prove or disprove the following: (a) If R is transitive & reflexive then R R - 1 is an equivalence relation. (b) If R is a partial order then R - 1 is a partial order. (c) ( R R - 1 ) * is an equivalence relation. 2. (4 points) Let P N × N be the relation where xPy holds if and only if x = y i for some i N . Is P a partial order? an equivalence relation? neither? 3. (4 points) Let be a partial order on some finite set V . Let G = ( V, E ) be a directed graph where E = { ( u, v ) | u v u = v } . Prove that G does not contain any directed cycles. [Why are there no
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern