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h1 - CS 241 Sect 001 Homework 1 Dr David Nassimi...

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CS 241, Sect 001 Homework 1 Dr. David Nassimi Foundations I Due: Week-3, Fri. Sep. 18 Fall 2009 Chapter 1: Sets and Logic 1. Let A = { 1 , 3 , 5 } and B = { 2 , 3 , 4 } . Determine each of the following sets. A B A B A - B B - A ( A B ) - ( A B ) ( A - B ) ( B - A ) 2. Prove the following set-equality, by using each of the methods described below. ( A B ) ( A B ) = ( A B ) ( A B ) (a) Proof using a Venn Diagram. (b) Algebraic proof. This method uses set-algebraic manipulations to prove the equality, using valid algebraic rules. The basic rules listed in the table below are assumed to have been proven, and thus are valid rules to use. Basic Rules (Equalities) in Set Algebra Associative Laws: ( X Y ) Z = X ( Y Z ) ( X Y ) Z = X ( Y Z ) Commutative Laws: X Y = Y X X Y = Y X Distributive Laws: X ( Y Z ) = ( X Y ) ( X Z ) X ( Y Z ) = ( X Y ) ( X Z ) De Morgan’s Laws: X Y = X Y X Y = X Y Complement Laws: X X = U X X = φ X = X Repetition: X X = X X X = X 0/1 Laws: φ = U U =

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h1 - CS 241 Sect 001 Homework 1 Dr David Nassimi...

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