# CMPSC360hw5 - Name Section CMPSC 360 Fall 2008 Homework 5:...

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Name Section CMPSC 360 Fall 2008 Homework 5: PRACTICE EXAM 1 HOMEWORK 5 IS DUE AT THE BEGINNING OF CLASS ON WEDNES- DAY 10/1/2008. This is a CLOSED BOOK exam. You are allowed one single sided sheet of notes. NO electronic devices are allowed (no cell phones, music players, etc). Give reasons for all your answers. Good Luck! Problem Possible Points 1 25 2 25 3 25 4 25 Total 100 1

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1. (25 points) Logic, Quantiﬁers, Proofs (a) Let P ( x,y ) be the proposition, for integers x and y , that “ x + y = x - y ”. Which of the following statements are true? Explain each answer in one sentence. i. x y P ( x,y ) ii. y x P ( x,y ) iii. y x P ( x,y ) (b) Write the negation of the proposition in 1(a)iii above (that is, ¬ ∀ y x P ( x,y )) in terms of the proposition Q ( x,y ), which states that x + y 6 = x - y . (c) Prove that if a and b are rational, then ab is rational. (d) Prove that if
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## This note was uploaded on 10/08/2008 for the course CMPSC 360 taught by Professor Haullgren during the Fall '08 term at Pennsylvania State University, University Park.

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CMPSC360hw5 - Name Section CMPSC 360 Fall 2008 Homework 5:...

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