Handout 12

# Handout 12 - Mehran Sahami CS103B Handout#12 Problem Set#2...

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Mehran Sahami Handout #12 CS103B January 23, 2009 Problem Set #2 Due: 11:00am on Monday, February 2nd 1. Let R be a relation on the set {1, 2, 3, 4, 5} containing the ordered pairs: {<1,1>,<1,2>,<1,3>,<2,3>,<2,4>,<3,1>,<3,4>,<3,5>,<4,2>,<4,5>,<5,1>,<5,2>,<5,4>} Determine and write out the following relations: a) R 2 b) R 3 c) R 4 2. Let S be the set of ordered pairs of positive integers. That is S = {(x, y) | x and y are positive integers}. Let R be the relation on S such that <(a, b), (c, d)> R if and only if ad = bc. Prove that R is an equivalence relation. 3. Prove or disprove: the symmetric closure of the reflexive closure of the transitive closure of any relation is always an equivalence relation. 4. Given relation R = {<a,a>,<a,b>,<a,c>,<a,d>,<b,b>,<c,b>,<c,c>,<c,d>,<d,b>,<d,d>} on the set S = {a, b, c, d}. Is R a partial order? If so, draw the Hasse diagram for R . If not, explain why. 5.

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Handout 12 - Mehran Sahami CS103B Handout#12 Problem Set#2...

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