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Homework 1 Solutions - Solutions to CS191 Homework One...

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Solutions to CS191 Homework One Winter 2007 Due: Jan. 30, 2007, in class Section 1.1, p7 Determine whether each sentence in Exercises 1-8 is a proposition. If the sentence is a proposition, write its negation. (you are not being asked for the truth values of the sentences that are propositions.) Exercise (3) For some positive integer n , 19340 = n 17 Answer: It is a proposition. Negation: For every positive integer n , 19340 n 17. Write the truth table of each proposition in Exercises 19-26 Exercise (26) ¬ ( p q ) ( ¬ q r ) Answer : p q r ( p q ) ¬ ( p q ) ¬ q ( ¬ q r ) ¬ ( p q ) ( ¬ q r ) T T T T F F T T T T F T F F F F T F T F T T T T T F F F T T T T F T T F T F T T F T F F T F F T F F T F T T T T F F F F T T T T In exercises 36-40, formulate the symbolic expression in words using p: Today is Monday. q: It is raining. r: It is hot. Exercise (38) ¬ ( p q ) r Answer : 1
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It is not the case that (today is Monday or it is raining) and it is hot. (This answer is not clear enough. A better way to say is It is hot and it is not the case that (today is Monday or it is raining). In exercises 47-52, represent the proposition symbolically by letting p: You heard the “Flying Pigs” rock concert. q: You heard the “Y2K” rock concert. r: You have sore eardrums. Exercise (51) You did not hear the “flying Pigs” rock concert and you did not hear the “Y2K” rock concert, but you have sore eardrums. Answer: ¬ p ∧¬ q r . Section 1.2, p16 Assuming that p and r are false and that q and s are true, find the truth value of each proposition in Exercises 10-17. Exercise (14) ( p q ) r Answer : p ( q r ) = (F T) F = T F = F. In Exercises 38-41, write each conditional proposition symbolically. Write the converse and contrapositive of each proposition symbolically and in words. Also, find the truth value of each conditional proposition, its converse, and its contrapositive.
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