MIT6_042JF10_rec11

MIT6_042JF10_rec11 - 6.042/18.062J Mathematics for Computer Science Tom Leighton and Marten van Dijk Problems for Recitation 11 1 Give a

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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
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This note was uploaded on 01/19/2012 for the course CS 6.042J / 1 taught by Professor Tomleighton,dr.martenvandijk during the Fall '10 term at MIT.

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MIT6_042JF10_rec11 - 6.042/18.062J Mathematics for Computer Science Tom Leighton and Marten van Dijk Problems for Recitation 11 1 Give a

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