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MATH 240 MidtermMcGill UniversityInstructors:J. Macdonald, A. LumleyDate:February 18, 2020Family 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 areforbidden.•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 atheorem, 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 andindicate that you are doing so.1
Q1/20Q2/ 20Q3/20Q4/ 20Total/ 801.[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 variablesx, y, zare from:8x9y(x < y)^⇣8z((xz)^(zy))=)((z=x)_(z=y))⌘!(c) [6 points] Letxbe an irrational number and letrbe a rational number. Prove thatx+ris irrational.2bYuen'sIgn
Continuation of Question 13cproofbycontradictionSupposeXtrCQThenIamcIstxtrIbNowreQFCidC