MATH 240 Winter 2020 Midterm.pdf.pdf - MATH 240 Midterm...

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MATH 240 Midterm McGill University Instructors: J. Macdonald, A. Lumley Date: February 18, 2020 Family name: First name: ID number: Section: TR 11:35 MAASS 112 (Dr. Jeremy Macdonald) TR 4:05 ENGMC 204 (Dr. Allysa Lumley) Instructions: You are allowed 2 hours to complete this exam. This is a closed-book exam. Calculators or other electronic devices are forbidden . You are expected to justify all statements that you make. You may use any theorem stated in class, unless you are being asked to prove that theorem. When you use a theorem, you should state that you are doing so. Your solutions must be clearly written and use proper notation, where applicable. If you need additional space, please use the back of the previous page and indicate that you are doing so . 1
Q1 /20 Q2 / 20 Q3 /20 Q4 / 20 Total / 80 1. [20 points] Logic and proofs. (a) [6 points] Write down a truth table for the logical expression ( ( p _ ¬ q ) ^ r ) = ) ( p () ( q ^ r ) ) (b) [8 points] Prove or disprove the following statement, where the variables x, y, z are from : 8 x 9 y ( x < y ) ^ 8 z ( ( x z ) ^ ( z y ) ) = ) ( ( z = x ) _ ( z = y ) ) ! (c) [6 points] Let x be an irrational number and let r be a rational number. Prove that x + r is irrational. 2 b Yuen's Ign
Continuation of Question 1 3 c proof by contradiction Suppose Xtr C Q Then I am c I s t xtr I b Now re Q F Cid C

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