Week 2 Tutorial

# Week 2 Tutorial - message b To be a citizen of this country...

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CONCORDIA UNIVERSITY COMP 232/2 Mathematics for Computer Science FALL 2010 Tutorial Problems (Section DD) : Week 2 2-1. Which of these are propositions? a) Do not pass go. d) There are no black ﬂies in Quebec. b) What time is it? e) The moon is made of green cheese. c) 4 + x = 5. f) 2 n 100. What are the truth values of those that are propositions? 2-2. Assume knights always tell the truth and knaves always lie, and assume A is either a knight or a knave and B is either a knight or a knave. a) Suppose A says “At least one of us is a knave” and B says nothing. i) Is A a knight? iii) Is B a knight? ii) Is A a knave? iv) Is B a knave? b) Suppose A says “The two of us are both knights” and B says “A is a knave”. v) Is A a knight? vii) Is B a knight? vi) Is A a knave? viii) Is B a knave? In each case, if you cannot determine what these two people are, can you draw any conclusions? 2-3. Rewrite each of these statements in the form “if p then q ”. a) I will remember to send you the address only if you send me an e-mail
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Unformatted text preview: message. b) To be a citizen of this country it is suﬃcient that you be born in Canada. c) You will ﬁnd your textbook to be a useful reference should you choose to keep it. d) For the Canadiens to win the Stanley Cup it is necessary that their goalie play well. e) That you got the job implies you had the best credentials. + The logical operators ↑ ( nand ), ↓ ( nor ), and ± ( nimp ) are deﬁned as follows. P Q P ↑ Q P ↓ Q P ± Q T T F F F T F T F T F T T F F F F T T F 2-4. Let p, q, r be the propositions p : You have the ﬂu ; q : You will suﬀer ; r : You will recover . Express each of these propositions as an English sentence. i) p → q iii) q ↑ r v) ( p ↑ r ) ∨ ( q ↑ r ) ii) q ⊕ r iv) p ∨ q ∨ r vi) ( p ∧ q ) ∨ ( r ± q ) 2-5. The eight binary logical operators are ∧ , ∨ , → , ↔ , ↑ , ↓ , ± , ⊕ . For each binary logical operator \$ , determine whether \$ satisﬁes ( p \$ q ) ∧ ( q \$ p ) ≡ p ↔ q. 10-Sep-2010, 11:35 am...
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## This note was uploaded on 11/15/2010 for the course ENCS COMP 232 taught by Professor Ford during the Fall '10 term at Concordia University Irvine.

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