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MIT6_042JF10_rec11

MIT6_042JF10_rec11 - 6.042/18.062J Mathematics for Computer...

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6.042/18.062J Mathematics for Computer Science October 15, 2010 Tom Leighton and Marten van Dijk Problems for Recitation 11 1. Give a description of the equivalence classes associated with each of the following equivalence relations. (a) Integers x and y are equivalent if x y (mod 3). (b) Real numbers x and y are equivalent if x = y , where z denotes the smallest integer greater than or equal to z . 2. Show that neither of the following relations is an equivalence relation by identifying a missing property (reflexivity, symmetry, or transitivity). (a) The “divides” relation on the positive integers. (b) The “implies” relation on propositional formulas.
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2 Recitation 11 3. Here is prerequistite information for some MIT courses: 18 . 01 6 . 042 18 . 01 18 . 02 18 . 01 18 . 03 6 . 046 6 . 840 8 . 01 8 . 02 6 . 01 6 . 034 6 . 042 6 . 046 18 . 03 , 8 . 02 6 . 02 6 . 01 , 6 . 02 6 . 003 6 . 01 , 6 . 02 6 . 004 6 . 004 6 . 033 6 . 033 6 . 857 (a) Draw a Hasse diagram for the corresponding partially-ordered set. (A Hasse diagram is a way of representing a poset
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