Inclusion-Exclusion PrincipleDate: 09/03/2002 at 19:56:57 From: Rehana Chandarpal Subject: Sets In a survey of 100 people, 85 like calypso and 93 like pan. Calculate the number of people who like both calyso and pan. I tried answering this question by doing the equation that my teacher showed me but I still can't do it. Date: 10/18/2002 at 17:27:22 From: Doctor Nitrogen Subject: Re: Sets Hi, Rehana: Why don't we let a capital letter like X denote a set? And we'll use #X to denote the number of elements in set X. Let U be the set with 100 people in it, let A be the subset of U that has all the people who like calypso, let B be the subset of people in U who like pan, and let C be the subset of people in U who like both calypso and pan. Then #U = 100. #A = 85 #B = 93 #C = (unknown). To find #C, use the fact that the total number of people in U equals the total number of people in A plus the total number of people in B, minus the total number of people in C, so #U = #A + #B - #C or 100 = 85 + 93 - #C Can you figure the rest out now? This way of solving a math problem like this one uses what is called the "Inclusion-Exclusion Principle." Here it uses the fact that #U = #(A u B) - #(A intersection B). The lower case "u" denotes "union." Did this help answer the question you had concerning your mathematics problem? You are welcome to return to The Math Forum/Doctor Math whenever you have any math related questions. - Doctor Nitrogen, The Math Forum http://mathforum.org/dr.math/ |
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