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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