CSC165H1F Homework Exercise # 4 Fall 2011
Worth: 2% Due: By 10pm on Friday 28 October.
Remember to write your full name, student number, and CDF/UTOR email address prominently
on your submission.
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.
To solve each of the problems in this exercise, use a proof structure that has been shown in lectures. Explain what
you are doing (and why) at each step in your proofs. Start by translating each statement into symbolic notation.
1. Consider the following:
2 2
Theorem ? Suppose m is an even integer and n is an odd integer. Then n ▯ m = n + m:
After introducing the predicates E(i) : i is an even integer and O(i) : i is an odd integ

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