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### m256-9-18

Course: M 256, Fall 2007
School: Calvin
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256 Mathematics September 18 &amp; 19, 2008 1. Sets (Rosen, 2.1 &amp; 2.2) Terminology. Set, element, empty set, subset, proper subset, set equality. Be sure you distinguish between and . (For example, 1 Z and {1} Z, but {1} Z.) The distinction between and is less important. / Describing a set. (1) Using a roster; e.g., A = {1, 2, -1, 0, 2, -1, 1, 0}. (2) Using set builder notation; e.g., B = {n Z |...

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256 Mathematics September 18 & 19, 2008 1. Sets (Rosen, 2.1 & 2.2) Terminology. Set, element, empty set, subset, proper subset, set equality. Be sure you distinguish between and . (For example, 1 Z and {1} Z, but {1} Z.) The distinction between and is less important. / Describing a set. (1) Using a roster; e.g., A = {1, 2, -1, 0, 2, -1, 1, 0}. (2) Using set builder notation; e.g., B = {n Z | -2 n 1}. Making new sets from old. (1) Power set. P(A) = {S | S A} (2) Cartesian Product. A B = {(a, b) | a A and b B} Set operations. (1) Union. A B = {x | (x A) (x B)} (2) Intersection. A B = {x | (x (x A) B)} (3) Set difference. A - B = {x | (x A) (x B)} / / (where U is the universal set) (4) Complement. A = U - A = {x | x A} De Morgan's laws, v.3.0. (1) A B = A B (2) A B = A B More terminology. Disjoint sets, cardinality (of a finite set). 2. Functions (Rosen 2.3) Terminology. Function, domain, codomain, range. Definition. A one-to-one function is Defini...

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