For Discrete Math II, Assignment 1, Relations and Properties. Seeking help with the assignment. The instructions are on the file attached and explained appropriately. These questions are really not hard to work on, just don't have the time at the moment to work on them as I have other classes to attend to which deadlines are approaching fast so please assist if possible.

 

MAD 3105 Assignment 01NAME:_______________________________________________Relations and Their PropertiesDUE: Thursday, January 14th(11:59pm EST)Directions:Show ALL work for credit. There are 5 questions. Write on your own paper.Each part is worth 5 points, unless stated otherwise. You may type or neatly write yoursolutions.Make sure you write your name on all papers that you use.Scan this page at thefront of your work, and compile as ONE .pdf file.Check that all work was saved andscanned legibly.Save your file as:A01xyLASTNAME.pdf.(where “xy” is your first and middle initial)Once completed, attach your file under “Assignment 01” on Blackboard and click“submit.”Thank you!1) For the relation?= {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)}on the set±= {1, 2, 3, 4}, explain/show whether or not the relation is the following:(For any credit, be sure to give a reason why for each).(a) reflexive,(b) symmetric,(c) antisymmetric,(d) transitive.2) Let the sets be relations on the real numbers:?1= {(²,³)∈ ℝ2|² ≥ ³},the“greater than or equal to” relationand let?2= {(²,³)∈ ℝ2|² ≠ ³},the “unequalto” relation.Find:(10 pts each)(a)?1∩ ?2(write out the relation in the set notation, as?1and?2were written)(b)?1− ?2(write out the relation in the set notation, as?1and?2were written)(c)?1⨁?2(write out the relation in the set notation, as?1and?2were written)3)(a) How many relations are on the set{²,³,´}?(b) If?= {(1, 1), (1, 2), (2, 4), (3, 1), (3, 0)}&µ= {(1, 2), (2, 0), (3, 1), (0, 0), (4, 3)}findµ ∘ ?4)?is the relation represented by the matrix¶·=100111010¸, find the matrix for:(a)?¹1(b)?º º(c)? ∘ ?(i.e.?2)5) (a) The relation R is on{1, 2, 3}.Represent the relation(10 points)?= {(1, 1), (2, 1), (2, 2), (2, 3), (3, 2)}with a matrix.(b) By looking at the matrix, is the relation R reflexive? Why or why not?(5 points)(c) Draw the directed graph that represents the relation R.(10 points)

Attachments:

• 1495865306-Assignment 1.pdf