# assn1 - CONCORDIA UNIVERSITY DEPARTMENT OF COMPUTER SCIENCE...

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

CONCORDIA UNIVERSITY DEPARTMENT OF COMPUTER SCIENCE & SOFTWARE ENGINEERING COMP 232/2 Mathematics for Computer Science FALL 2010 Assignment 1 1. (10 marks) Professor Smullyan went to a remote island where all inhabitants were either knights or knaves. Knights always tell the truth and knaves always lie. While he was visiting the island, he came across two of the inhabitants, A and B, resting under a tree. Professor Smullyan asked them, “Is either of you a knight?” and A responded to his question. The professor immediately knew what both A and B were. What were A and B? How did the professor figure it out? 2. (15 marks) Classify each of the following as a contradiction, a tautology, or a contingency. a) ( p q ) ( ¬ ( p q )) b) ( p q ) ( q r ) ∨ ¬ r p c) ( p r ) ( p ∨ ¬ r ) F 3. (15 marks) Prove the following logical equivalences without using truth tables. a) ( ¬ p F ) p T b) ( p q ) ( ¬ p r ) ( q r ) T c) ( p q ) ( ¬ q r ) (( ¬ q r ) q ) q 4. (20 marks) Let P ( x, y
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