hw6 - R over the powerset 2 { 1 , 2 , 3 } , determine if it...

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CSE 20: Discrete Mathematics Fall 2010 Problem Set 6 Instructor: Daniele Micciancio Due on: Fri Nov 19, 2010 In addition to the problems below, you should also solve the following problems from the textbook for additional training, but without submitting your answers: Section 2.5 (1,2,4,18), Section 3.1 (1,3,8,13,19), Section 3.2 Problem 1 (12 points) Consider the following computer program: int f(int x, int y) { if (x==0) then return y else return f(x-1,y+3) } Assume that the program if always called on nonnegative integer inputs. 1. What’s the output of f(2,0)? f(3,0)? f(3,1)? 2. Can you express the output of f(x,y) as a simple formula involving x and y? 3. Prove by induction that your answer given in part 2 is correct. Problem 2 (12 points) For each of the following relations
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Unformatted text preview: R over the powerset 2 { 1 , 2 , 3 } , determine if it is a partial order relation. If so, list its maximal elements. If not, says which properties (reexive, antisymmetric and transitive) it fails to satisfy. (If it fails more than one property, list all of them.) 1. ( A,B ) R if and only if B \ A = . (Remember that \ is the set dierence operation.) 2. ( A,B ) R if and only if A \ B 6 = 3. ( A,B ) R if and only if A 3 | B | , where A is the sum of the elements in A , and | B | is the size of the set B . 4. ( A,B ) R if and only if 3 | A | B , where A is the sum of the elements in A , and | B | is the size of the set B ....
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This note was uploaded on 01/08/2011 for the course CSE cse105 taught by Professor Cs during the Fall '10 term at UCSD.

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