ans55-mt1 - Math 55. Sample Answers to First Midterm There...

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Math 55. Sample Answers to First Midterm There may be other correct solutions to these problems. 1. (8 points) Use rules of inference to show that the hypotheses: “Today is Valentine’s Day,” “If today is Valentine’s Day then Fred buys chocolate on his way to campus (today),” and “Every day, if Fred oversleeps then he does not buy chocolate on his way to campus” imply the conclusion “Fred did not oversleep today.” Let p be “Today is Valentine’s Day,”, let q ( d ) be “Fred buys chocolate on day d , and let r ( d ) be “Fred oversleeps on day d .” Then our argument is: Step Reason 1. p Premise 2. p q (today) Premise 3. q (today) Modus Ponens using (1) and (2) 4. ¬¬ q (today) Double negation rule 5. d ( r ( d ) → ¬ q ( d )) Premise 6. r (today) → ¬ q (today) Universal instantiation of (4) 7. ¬ r (today) Modus Tollens using (4) and (6) 2. (9 points) For each of the following functions, determine: (i) whether it is 1 - 1 , (ii) whether it is onto, and (iii) whether it has an inverse. Briefly justify each answer (this does not have to be a proof). (a).
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This note was uploaded on 03/08/2010 for the course MATH 55 taught by Professor Strain during the Spring '08 term at University of California, Berkeley.

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ans55-mt1 - Math 55. Sample Answers to First Midterm There...

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