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# ps6 - Massachusetts Institute of Technology 6.042J/18.062J...

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Massachusetts Institute of Technology 6.042J/18.062J, Spring ’11 : Mathematics for Computer Science March 14 Prof. Albert R Meyer revised Monday 14 th March, 2011, 23:00 Problem Set 6 Due : March 30 Reading: Chapter 9.5 9.9 , Partial Orders; Chapter 11 11.6 , Simple Graphs. Skip Chapter 10 , Communication Nets, which will not be covered this term. Problem 1. Let R 1 , R 2 be binary relations on the same set, A . A relational property is preserved under product, if R 1 R 2 has the property whenever both R 1 and R 2 have the property. (a) Verify that each of the following properties are preserved under product. 1. reflexivity, 2. antisymmetry, 3. transitivity. (b) Verify that if either of R 1 or R 2 is irreflexive, then so is R 1 R 2 . Note that it now follows immediately that if if R 1 and R 2 are partial orders and at least one of them is strict, then R 1 R 2 is a strict partial order. Problem 2. The most famous application of stable matching was in assigning graduating medical students to hospital residencies. Each hospital has a preference ranking of students and each student has a preference order of

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ps6 - Massachusetts Institute of Technology 6.042J/18.062J...

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