# H3 - CS123 Youssef March 4 2010 Homework 3 Due Date Problem...

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CS123 March 4, 2010 Youssef Homework 3 Due Date: March 30, 2010 Problem 1: (20 points) For each of the following 4 relations on the set L of all living people on Januray 1, 2010, state (no proof necessary) if the relation is reﬂexive, symmetric, antisymmetric, transitive, equivalence relation, and/or partial order. In the case of equivalence relations, explain what every equivalence class signiﬁes. In the case of partial orders, indicate if the set L has a minimum, a maximum, minimals, and/or maximals, and explain what minimum, maximum, minimal and maximal mean in that context. a) x R y if x is taller than y or x is the same person as y. b) x R y if x and y have the same ﬁrst name. c) x R y if x graduated from the same university as y. d) x R y if the annual income of x is less than that of y or x is the same person as y. Problem 2: (20 points) Let f be a real-variable function where f ( x ) = x 2 + 2 x + 5, and let E = {- 5 , - 4 , - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 , 5 } . Deﬁne the relation

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H3 - CS123 Youssef March 4 2010 Homework 3 Due Date Problem...

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