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Unformatted text preview: Fall 2007 ARE211 Problem Set #04 First Graphical Problem Set Due date: Oct 02 (1) Some quick multiple choice questions on necessary and sufficient conditions. (a) The most important question to ask in determining whether x is sufficent for y is: (i) Can you have y without having x ? (ii) Does x have any relevance for y ? (iii) Does having x ensure that you will have y ? (iv) If you know that you have y , do you know that you will have x ? Justify your answer using the fact that if x is sufficient for y then the set of objects satisfying x is contained in the set of objects satisfying y . (b) The most important question to ask in determining whether p is necessary for q is: (i) Can you have p without having q? (ii) Does having p ensure that you will have q? (iii) Can p and q both be true at the same time? (iv) Do you have to have p in order to have q? Justify your answer using the fact that if p is necessary for q then the set of objects satisfying p contains the set of objects satisfying q . (2) Consider the following three class of triangles: (A) Isoceles (B) Equilateral (C) Right-angled Now answer the following questions 1 2 (a) Which class of triangle is sufficient for one of the other classes? Explain your answer. (b) Which class of triangle is necessary for one of the other classes? Explain your answer. (c) Is it possible to identify a restriction on one of the angles in the remaining class of triangles such that if this additional restriction is satisfied, then this class is sufficient for another class? If yes, identify the condition. If no, explain in terms of set theory.for another class?...
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- Fall '07