HW3-Solutions

HW3-Solutions - EECS 203 DISCRETE MATHEMATICS Homework 3...

This preview shows pages 1–2. Sign up to view the full content.

EECS 203: DISCRETE MATHEMATICS Homework 3 Solutions 1. Chapter 1.5, Problem 24 From the statement “ P ( c ) Q ( c )” one cannot conclude that “ P ( c )” is true. (The simplification inference says that given “ P ( c ) Q ( c )” one can conlclude that “ P ( c )” is true.) 2. Chapter 1.5, Problem 28 1. x ( P ( x ) Q ( x )) premise 2. x (( ¬ P ( x ) Q ( x )) R ( x )) premise 3. x ( P ( x ) ∨ ¬ Q ( x ) R ( x )) DeMorgan, defn. of (line 2) 4. P ( c ) Q ( c ) universal instantiation (line 1) 5. ( P ( c ) R ( c )) ∨ ¬ Q ( c ) universal instantiation (line 3) 6. P ( c ) R ( c ) resolution, idempotency of (lines 4,5) 7. ¬ R ( c ) P ( c ) defn. of (line 6) 8. x ( R ( x ) P ( x )) universal generalization (lines 4,5,7) 3. Kevin Bacon is an actor. Kevin Bacon has a Bacon number of 0 and is the only person with this Bacon number. Anyone who has appeared in the same movie as another person with a Bacon number has a Bacon number. A person has Bacon number i +1 if and only if he or she has appeared in a movie with someone whose Bacon number is i , but never with a person whose Bacon number is less than i . Use set notation to define B i : the set of people with bacon number i . (Use the predicate A ( p, m ), “person p has appeared in movie m ”.) Start with B 0 and B 1 . Let M ( a, b ) be the predicate that persons a and b have appeared in a common movie: M ( a, b ) ≡ ∃ m ( A ( a, m ) A ( b, m )) From the definition of Bacon numbers we have: B 0 = { KevinBacon } B 1 = { a | M ( a, KevinBacon ) a = KevinBacon }

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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