1. Objectives: By the end of class, I will be able to:  Identify sets  Understand subsets, intersections, unions, empty sets, finite and infinite sets, universal sets and complements of a set

2. SETS Set – a well defined collection of elements A set is often represented by a capital letter. The set can be described in words or its members or elements can be listed with braces { }. Example: if A is the set of odd counting numbers less than 10 then we can write: –A = the set of all odd counting numbers less than ten OR –A = {1,3,5,7,9 } –To show that 3 is an element of A, we write: 3 A –To show 2 is not an element of A, we write : 2  A

3. SETS If the elements of a set form a pattern, we can use 3 dots. Example: {1,2,3… } names the set of counting numbers Another way to describe a set is by using set-builder notation. Example: { n | n is a counting number } This is read – the set of all elements n such that n is a counting number.

5. SETS Finite set – a set whose elements can be counted, and in which the counting process comes to an end. Examples: –The set of students in a class – {2,4,6,8…..200} – {x | x is a whole number less than 20} Infinite set – a set whose elements cannot be counted Examples: –The set of counting numbers – { 2,4,6,8… } Empty set or null set, is the set that has no elements Examples: –The set of months that have names beginning with the letter Q – { x | x is an odd number exactly divisible by 2 } Symbol for the empty set { } or Ø Universal set - is the entire set of elements under consideration in a given situation and is usually denoted by the letter U. Example: –Scores on a Math test. U = {0,1,2 …100 }

6. SETS Subsets – set A is a subset of B if every element of set A is an element of set B. We write: A  B Example: –the set A = {Harry, Paul } is a subset of the set B = {Harry, Sue, Paul, Mary } –The set of odd whole numbers {1,3,5,7… } is a subset of the set of whole numbers, {0,1,2,3… }

8. SETS Union – is the set of all elements that belong to set A or to set B, or to both set A and set B. Symbol: A υ B Example: –If A = {1,2,3,4 } and B = { 2,4,6 }, then A υ B = {1,2,3,4,6} Intersection - is the set of all elements that belong to both sets A and B. Symbol: A ∩ B Example: –If A = {1,2,3,4,5} and B = {2,4,6,8,10} then A ∩ B = { 2,4 }

9. SETS Complement – is the set of all elements that belong to the universe U but do not belong to the set A. Symbol: A or A c or A` all read A prime Example: –If A = {3,4,5} and U = {1,2,3,4,5}, then A c = { 1,2 } Practice with sets

11. Set notation Let’s review and look at Notes from regentsprepNotes

12. Set notation Let’s practicepractice