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# Math 105 notes on several definitions and how to find everything relating to sets!. Math 105-09

WSU

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This 3 page Class Notes was uploaded by Emily Padilla on Thursday February 19, 2015. The Class Notes belongs to Math 105-09 at Washington State University taught by in Spring2015. Since its upload, it has received 91 views. For similar materials see Exploring Mathematics in Math at Washington State University.

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Date Created: 02/19/15

Math 105 Notes One week of Notes De nitions Eements of a set A collection of objects Objects belonging to a set Commonly demoted with a capital letter S 1234 Set with no elements is an empty set denoted by 0 Cardinality Number of elements in a set Cardinality of a set A a bc Denoted as an A read as 39n of A or of elements in Set A NA 9 Subsets of a set Set A the subset of B if every element in A is found in set B Set inside a set A cB Equality of Sets Set A is egual to set B provided the following conditions 1 Every element of A Element of B l A cB 2 Every element of B Element of A l B cA Symbols I Such That Q Set with no elements 6 Element of a set N Natural Numbers 1234 W Whole Numbers 0123 Z lntegers 3210123 Q Rational Numbers pq R Irrational Numbers n Element not part of a set Symmetric Difference Union Things that are in either set Intersection Taking things that are in A but that are also in B Upside Down Capitalized A For All There Exists Subset of e A u n 9 El Q Combining Symbols A A B Symmetric Difference A u B Things that are in either set A u B xleA or x B A n B Taking things from A that are also in B xleA and x B A x B First number comes from A Second number comes from B A x B aba B b B Method of Designating Sets 1 Description of Word A is set of even 5 from 19 2 Listing Roster Method A 2468 or E2468 3 SetBuilder Notation the set of even natural numbers A x x is even number between 1 and 9 A x 15x59 x is even and A xl2sx58 x 2n for some integer n Ex List all elements of each set using listing method lSet A of counting numbers between 10 and 20 A 111213141516171819 lSet B of letters in word 39Bumblebee B bumle Do not repeat Letters lC xlx is an even multiple of 5 that is less than 10 Do not include 10 C Q Ex Denote each set by setbuilder notation using x variable lSet A of counting numbers between 10 and 20 A xlx is a counting number 10 lt x lt 20 lSet of letters in word 39bumblebee B xlx is letter in 39bumblebee DC 4812 C xlx is a multiple of 4 between 4 and 12 inclusive Find cardinality of each set lSet A of counting numbers between 10 and 20 nA 9 A 111219 lSet B of letters in word 39bumblebee nB 5 DC xlx is an even multiple of 5 that is less than 10 nc 0 nQ 0 Subsets of a set Set A the subset of B if every element in A is found in set B A cB Ex A 123B gt A AcB 123 is in both set A and B resulting in a subset Equality of Sets Set A is equal to set B provided the following conditions 1 Every element of A Element of B l A cB 2 Every element of B Element of A l B cA Ex A eYEWS S Same Set B 2 How to Combine Sets A 12 B 23 l Symmetric Difference A A B 13 lj Union A u B 123 lj lntersect A n B 2 l A cross B A x B 12 13 22 23 Practice Problems If A 7 how many subsets does A have How many two digit numbers that end in 3 or 7 are there How many marbles are there if there are 3 blue 10 red 1 that is both fA2andB3whatis aAuB bAxB

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