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Computer Science
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Nathalie Fournier

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CSC165H1Y Homework Exercise # 4 Summer 2012 Worth: 3% Due: By 3 pm on Tuesday July 3. Remember to write the the full name and student number of each member of your group promi- nently on your submission. Your submission must be a PDF ▯le named e4.pdf and it must be handed-in using the MarkUs system. You may create the PDF ▯le using a typesetting system (export to PDF) or by scanning in handwritten work to create a PDF ▯le. Each exercise may be completed in groups of 1 { 2 students. Please read and understand the policy on Collaboration given on the Course Information Sheet. Then, to protect yourself, list on the front of your submission every source of information you used to complete this homework (other than your own lecture and tutorial notes, and materials available directly on the course webpage). For example, indicate clearly the name of every student with whom you had discussions, the title of every additional textbook you consulted, the source of every additional web document you used, etc. For each question, please write up detailed answers carefully. Make sure that you use notation and terminology correctly, and that you explain and justify what you are doing. Marks will be deducted for incorrect or ambiguous use of notation and terminology, and for making incorrect, unjusti▯ed, ambiguous, or vague claims in your solutions. Warning: this exercise is deceptively short. The proof, however, is relatively complicated, and will require understanding and being able to use a variety of inference rules (it might be a good idea to review them). A straightforward way of proving might not always work, and you will need to explore alternatives. You have two weeks to complete the exercise: please start early and plan to spend considerable time on it. That way you will
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