# Mad2104final exam page 8 of 8 17 10 pts the following

This preview shows page 8. Sign up to view the full content.

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:
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern