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Mad2104final exam page 8 of 8 17 10 pts the following

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MAD2104/Final Exam Page 8 of 8 17. (10 pts.) The following is a valid argument: "Each of five friends, Larry, Moe, Curly, Samantha, and Anitra, has taken a course in discrete mathematics and passed with a grade of at least a C. Every student who has taken and passed a discrete math class with a grade of at least a C can take a course in algorithms. Therefore, all five friends can take a course in algorithms." The validity of the argument can be seen easily by symbolizing the argument using propositional functions and quantifiers as follows: Define propositional functions as follows: f(x) : "x is one of the friends listed." d(x) : "x has taken and passed discrete math with at least a C." a(x) : "x can take a course in algorithms." Then the argument translates into this: ( x)(f(x) d(x)) ( x)(d(x) a(x)) ( x)(f(x) a(x)) In the proof of validity which follows provide the justification(s) for each step. In doing this, you should explicitly cite rules of inference and quantification, hypotheses, and preceding steps by number. 1. ( x)(f(x) d(x)) Justification: 2. f(y) d(y) Justification: 3. ( x)(d(x) a(x)) Justification: 4. d(y) a(y) Justification: 5. f(y) a(y) Justification: 6. ( x)(f(x) a(x)) Justification:
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