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Unformatted text preview: 1 ISyE 3770 Fall 2007 Homework #1 Solutions 1. Suppose U = [0 , 2], A = [0 . 5 , 1], and B = [0 . 25 , 1 . 5]. What are A B , A B , A B , and A B ? Solution: Note that A B . Then A B = [0 , 1 4 ) ( 3 2 , 2] A B = [0 , 1 4 ) [ 1 2 , 1] ( 3 2 , 2] A B = [0 , 1 2 ) (1 , 2] A B = [ 1 4 , 1 2 ) (1 , 3 2 ] 2 2. Prove DeMorgans Laws. You can use Venn diagrams or argue mathematically. Solution: Lets prove that A B = A B . Proof: x A B iff x / A B iff x / A and x / B iff x A and x B iff x A B 2 Now lets prove that A B = A B . Proof: x A B iff x / A B iff x / A or x / B iff x A or x B iff x A B 2 3. A box contains 3 marbles (one red, one green, and one blue). (a) Consider an experiment that consists of taking one marble from the box, then replacing it in the box, and then drawing a second marble from the box. What is the sample space?is the sample space?...
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This note was uploaded on 04/14/2008 for the course ISYE 3770 taught by Professor Goldsman during the Fall '07 term at Georgia Institute of Technology.
- Fall '07