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PART 1 MODULE 2 SET OPERATIONS, VENN DIAGRAMS SET …

PART 1 MODULE 2. PART 1 MODULE 2. SET OPERATIONS, venn DIAGRAMS . SET OPERATIONS. Let U = {x|x is an English-language film}. Set A below contains the five best films according to the American Film Institute. A = {Citizen Kane, Casablanca, The Godfather, Gone With the Wind, Lawrence of Arabia}. Set B below contains the five best films according to TV Guide. B= {Casablanca, The Godfather Part 2, The Wizard of Oz, Citizen Kane, To Kill A. Mockingbird}. Set C below contains the five most passionate films according to the American Film Institute. C = {Gone With the Wind, Casablanca, West Side Story, An Affair To Remember, Roman Holiday}. Notice that some films appear on more than one of these lists. SET INTERSECTION AND SET UNION. Casablanca and Citizen Kane are the films that are simultaneously in sets A and B. We say that {Casablanca, Citizen Kane} is the intersection of A and B. This is denoted: A B = {Casablanca, Citizen Kane}. Likewise, A C ={Gone With the Wind, Casablanca} B C = {Casablanca}.

A Venn diagram is a drawing in which geometric figures such as circles and rectangles are used to represent sets. One use of Venn diagrams is to illustrate the effects of set operations. The shaded region of the Venn diagram below corresponds to S ∩ T

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PART 1 MODULE 3 VENN DIAGRAMS AND SURVEY …

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injection. It is not a surjection because the range is not equal to the codomain. For example, there is no number in the domain with image 1 which is an element of the codomain. It is not an injection since more than one distinct element in the domain is mapped to the same element in the codomain. For example, f( 1) = f(1) but 1 6= 1 . Exercise ...

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Indeterminate Forms - Florida State University

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1 x) x= e.This is of the indeterminate form 1∞. We write exp(x) for exso to reduce the amount exponents. lim x→∞ (1 + 1 x)x= exp(ln( lim x→∞ (1 + 1 x)x)) = exp( lim x→∞ ln((1 + 1 x)x)) = exp( lim x→∞ xln(1 + 1 x)) = exp( lim x→∞ ln(1 + 1 x) 1/x) We can now apply L’Hopital’s since the limit is of the form 0 0. = exp ...

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