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# math 116 notes week 3 MATH 116

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This 3 page Class Notes was uploaded by Stacey Boateng on Sunday February 14, 2016. The Class Notes belongs to MATH 116 at Radford University taught by William Case in Spring 2016. Since its upload, it has received 16 views. For similar materials see Math and Humanity in Mathematics (M) at Radford University.

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Date Created: 02/14/16

Math 116: Introduction to set and set notation. Set: a collection of objects, things or numbers. The universal set it the set of all possible elements of a set used in the problem Denoted by: Examples of sets: 1,2,3,4,5,6,7 Ron, Phil, Kate, Nate Delaware, Virginia, California, Washington Roster Notation: all elements are listed one by one and separated by comas {1,5,7,9,11} {Mark, Matt, Millie} Builder Set Notation: {x|x is a description} Example: {x|x is an amino acid} Roster Notation Builder Set Notation {A,E,I,O,U} {x|x is a vowel} {Atlantic, Pacific, Indian} {x|x is an ocean} {3,6,9,12,14,16,18} {x|x is an odd number} Well Defined Set: A set is well defined if the elements of the set are clearly defined If a set is well defined, then there should not be any confusion of what the elements are in the set. Examples: x|x is a vowel: well defined x|x is a beautiful person: not well defined Write the following sets in builder set notation: {Virginia, Vermont}: {x|x is a state that begins with V} {1.4.9.16.25.36.40.64.81.100}: {x|x is a square} {Iowa, Utah, Ohio}:{x|x is a state with 4 letters} Write the following in roster set notation: {x|x is a state that begins with I}: {Indiana, Iowa, Idaho, Illinois} {x|x is a state that boarders Virginia}: {Maryland, West Virginia, Tennessee, North Carolina, Kentucky} Important Sets: Natural numbers/ counting numbers: N= {1,2,3,4….} Whole numbers: W= {0,1,2,3,4,5,6….} Integers: Z= {-5, -4, -3, -2, -1….} Important symbols: Empty Set: a set that contains no elements, also called the null set{} True of False: B {A,B,C,D,E}: True A {{A}, {B},{C},{D}}: False Equivalent Sets: they are equivalent if they have the same number of elements Example: {1,2,3} and {A, B, C} Symbol: Are the following sets equivalent? {A, B, C} {E, F, G} Subsets: A set B is a subset of C. every element in B is an element of C Symbolically B is a subset of c is written as: B C Example: Is A a subset of C? Yes, because every element in set A also Lies in set C A= {1,2,3,4,5} C= {1,2,3,4,5,6,7} Proper subset: A set B is a proper subset if C if every element of B is an element of set C and has at least one element that does not lie in set B Example: Is A a proper subset of C? A C, yes because every element that lies in set A also lies in set C with an extra element. A= {1,2,3,4,5} C= {1,2,3,4,5,6,7} List all of the possible subsets of {A, B, C} {A} {B} {C} {} {A,B} {B,C} {A,C} Number of elements in Set Subsets 0 0 1=2 1 2=2 1 2 4=2 2 3 3 8=2 4 16=2 4 5 32=2 5 6 6 64=2 Formula to find the number of subsets of a given set A with n elements: n S=2 S= 26 S=64 Example: how many subsets does a set with 10 elements have? S= 2n 10 S= 2 S= 1024

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