# f2004Exam - UNIVERSITY OF TORONTO FACULTY OF APPLIED...

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UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING ECE190F — Discrete Mathematics Final Examination December 6, 2004 Examiners: John Carter, Ben Liang Duration: 2.5 hours This is a “closed book” examination; no aids are permitted. No electronic or mechanical computing devices are permitted. Write your answers in the spaces provided. If necessary, use the backs of the pages for rough work. Show all steps and present all results clearly. State any assumptions that you may make. For full credit, answers to counting problems must be expressed as integers. Please write clearly; if we cannot read an answer, we cannot mark it. This examination has 11 pages (including this one). Be sure that you have a complete paper. Name Student Number MARKS Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Total Value 6 3 6 4 5 4 6 6 4 4 5 7 4 14 6 6 6 4 100 Mark Enter the frst letter oF your Family name here. 1

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1. (6 marks) Let A = { 1 , 2 , 3 , 4 , 5 } , B = { 3 , 6 } , and let E be the set of even integers. Find (a) A B (b) A - E (c) A E (d) P ( B ) (e) B × {∅} (f) ( B A ) ( B E ) 2. (3 marks) Let p and q be statements. Use a truth table to show that ( p q ) ( q →∼ p )i sa tautology. 3. (6 marks) Let F ( x ) mean that student x is a frosh, and let C ( x, y ) mean that student x is enrolled in class y , where the domain of x is the set of all students at U of T and the domain of y is the set of all classes at U of T.
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## This note was uploaded on 04/19/2008 for the course ECE 190 taught by Professor Carter during the Fall '06 term at University of Toronto- Toronto.

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f2004Exam - UNIVERSITY OF TORONTO FACULTY OF APPLIED...

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