{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

s09_a5 - (d History students are Arts students Prove that(d...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
UNIVERSITY OF WATERLOO School of Computer Science CS245 Logic and Computation Spring 2009 ASSIGNMENT 5 (Due: Thursday, July 9, 2009 at 5:00pm) Use makeCover to produce a cover page for your assignment and hand in your assignment in the CS245 assignment box. Assignments are to be done individually. 1. (6) Prove that: 2 2 n - 1 is divisible by 3 for all n 0. 2. (10 marks—1 for each formalization; 6 for proof) Using appropriate sets, formalize the following sentences. Your answers must not contain logical quan- tifiers. (a) Computer Science students are not History students. (b) No student is a Psychology student and not an Arts student. (c) Any student who is not a Computer Science student is a Psychology student.
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (d) History students are Arts students. Prove that (d) logically follows from (a)-(c) using natural deduction. In your proof you may use any of the inference rules from propositional and predicate logic and you may use any of the definitions given on the summary sheet for set theory. 3. (9 marks) Assume that S and T are binary relations. Prove the following predicates or give counter examples showing why they are not valid. • dom ( S ∩ T ) ⊆ ( dom S ) ∩ ( dom T ) • ( dom S ) ∩ ( dom T ) ⊆ dom ( S ∩ T ) 4. (9 marks) Prove or disprove the following property of binary relations. • id ( dom R ) = R ; R ∼...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern