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University of Toronto St. George
Computer Science
Nathalie Fournier

CSC165H1F Homework Assignment # 1 Fall 2011 Worth: 8% Due: By 10pm on Friday 7 October. Remember to write the full name, student number, and CDF/UTOR email address of each group member 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 (other than group members), 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. [20] 1. Let G denote the set of video games. Let Tetris and MarioKart be speci▯c games in G. Consider the following predicates, along with their meaning: C(x): \x is a console game"; W(x): \x is a web game"; P(x): \I have played/will play game x"; V (x;y): \x is more violent than y"; B(x;y): \x is better than y". Using only the domain, constants, and predicates above (in addition to appropriate connectives and quanti- ▯ers), translate each sentence below, i.e., give a natural English sentence that corresponds to each symbolic sentence, and give a clear symbolic sentence that corresponds to each English sentence. State clearly any assumptions you might need to make. (a) If I have played every console game, then I have played every web game. (b) 9x 2 G;9y 2 G;W(x) ^ B(y;x) ^ :P(y) (c) Some console game is more violent than every game that I have played. (d) 8x 2 G;W(x) ^ V (MarioKart;x) ) :P(x) (e) No console game that I have played is better than any web game. (f) 8x 2 G;C(x) ^ P(x) ) V (MarioKart;x) (g) I have played Tetris and MarioKart, and neither game is more violent than any web game. (h) 8x 2 G;8y 2 G;(9z 2 G;9w 2 G;W(z) ^ P(z) ^ B(x;z) ^ W(w) ^ P(w) ^ B(y;w)) ) V (x;y) (i) I will play Tetris, unless it is more violent than every console game I have played. (j) 9x 2 G;C(x) ^ P(x) ^ V (x;Tetris) ^ 8y 2 G;B(y;Tetris) ) V (x;y) [15] 2. Consider the following sentence about positive integers x and y: If xy is even, then x is even or y is even. For each sentence below, state whether it is the negation of, the converse of, the contrapositive of, unrelated to, or equivalent to the sentence above. Justify each of your answers brie y (
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