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MIT6_042JS10_lec09_prob

# MIT6_042JS10_lec09_prob - Massachusetts Institute of...

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Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science February 24 Prof. Albert R. Meyer revised February 24, 2010, 756 minutes In-Class Problems Week 4, Wed. Problem 1. Direct Prerequisites Subject 18.01 6.042 18.01 18.02 18.01 18.03 8.01 8.02 8.01 6.01 6.042 6.046 18.02, 18.03, 8.02, 6.01 6.02 6.01, 6.042 6.006 6.01 6.034 6.02 6.004 (a) For the above table of MIT subject prerequisites, draw a diagram showing the subject num- bers with a line going down to every subject from each of its (direct) prerequisites. (b) Give an example of a collection of sets partially ordered by the proper subset relation, , that is isomorphic to (“same shape as”) the prerequisite relation among MIT subjects from part ( a ). (c) Explain why the empty relation is a strict partial order and describe a collection of sets par- tially ordered by the proper subset relation that is isomorphic to the empty relation on ﬁve ele- ments —that is, the relation under which none of the ﬁve elements is related to anything. (d)

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MIT6_042JS10_lec09_prob - Massachusetts Institute of...

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