# Homework2 - COT 3100H Spring 2008 Homework#2 Assigned Due 1...

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COT 3100H Spring 2008 Homework #2 Assigned: 1/15/08 Due: 1/22/08 1) Prove that the fourth power of an odd integer leaves a remainder of 1 when divided by 16. (Hint: You may want to first prove that the expression a(a+1) or a(3a+1) is even for all integers a.) 2) Prove the following assertion: If x+y+z >120, then x > 40 or y > 40 or z > 40. 3) Prove this equality between two sets by using the laws of set theory AND the table method. A C A B C A A = ) ) ( ) (( 4) Let A, B and C be arbitrary sets. Prove that A (( (A B) (A C) ) ( ¬ B C)). 5) In each of these questions, assume that A, B and C are sets. a) Prove or disprove: ((A B) (B C)) (A C). b) Prove or disprove: ((A B) (A C)) ((B C) (C B)). c) Prove or disprove: If A B C , then either A B or A C . d) Prove or disprove: ( A - C ) ( C - B ) =

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Programming Option: If you do this program, skip the following written questions: 1, 2, 5abc
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Homework2 - COT 3100H Spring 2008 Homework#2 Assigned Due 1...

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