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# Class Note for MA 101 with Professor LaMaster at IPFW

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This 1 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Indiana University taught by a professor in Fall. Since its upload, it has received 15 views.

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Date Created: 02/06/15

Sets as a Basis for Whole Numbers A set is a collection of objects and the objects are called elements or members of the set The empty set or null set written or Q is the set without any members ie the set of all US states bordering Antarctica is the empty set A nonempty set is finite if it can have its elements listed where the list eventually ends while an infinite set goes on without end ie the set ofintegers 3 2 l 0 l 2 3 is in nite The cardinality of a nite setA written nA is how many members it has What is S if the set S consists of the letters in the word mathematics S How many members does it has nS Subset of a Set A QB and Proper Subset of a Set A CB SetA is a said to be a subset ofB written A QB if and only if every element ofA is an element ofB SetA is a said to be a proper subset ofB writtenA CB ifA QB and there is an element ofB that is not inA Example The set of the original thirteen colonies is a proper subset of e 1 the set of all US states 0 S The set of letters in the word math is a proper subset of the set of letters in the word mathematics m a t h C m a t h e i c s Union of Sets AU B The union of two setsA and B written A U3 is the set of all elements belonging to eitherA or to B or both What letters are in the word math or in the word class The union helps us answer that question IfA m a t h B c 1 a s then A U B m a t h c 1 s Intersection of Sets Am B The intersection of two setsA and B written Am B is the set of all elements common to setsA and B What letters are in the word math and in the word class The intersection helps us answer that question EA m a t h B 0 1 a 5 than A 33 a Two sets are disjoint if they have no elements in common d 0 What letters are in the word math and in the word dog g Complement of a Set A The complement of a setA writtenA is the set of all elements in the universe that are not inA ballquot i lfthe umverse 1s the set of the 26 letters of our alphabet l 1 O P the complement of the set of the letters in the word mathematics is qr u v the set of the letters of the alphabet not in the word mathematics WXY Z Exercises SupposeA 0 l B 1 2 3 C 0 l 2 Sketch a Venn Diagram to illustrate their relationship Insert the appropriate symbol 6 e g C or t in the blank to make a true statement 2 B A B C AUC 2 C A C A AnC Closure Property for Addition A set of numbers is closed under addition if the sum of any two elements including themselves is also in that set Which of the sets A B and C if any are closed under addition Similarly which of the sets A B and C if any are closed under subtraction Which of the sets A B and C if any are closed under multiplication Which ofthe sets A B and C if any are closed under division

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