2. Sets and Set Notation

3. What are sets? A set is a collection of things. The "things" in the set are called the "elements”. A set is represented by listing all the elements of the set.

4. EX: Set of colors in the rainbow The elements of this set are red, orange, yellow, green, blue, indigo, & violet. {red, orange, yellow, green, blue, indigo, violet} Sets are written using the roster method. Now the elements of our set are written:

5. There has to be more to it than that! Universal set: Set of all elements under consideration. Denoted by capital U U = {red, orange, blue, green, indigo, yellow} A = {red, green, blue} Subsets are parts of the universal set. They are labeled by capital letters Subset symbol

6. A picture representation looks like this A U red A : means red is an element of set A Symbol for element

7. U = set of all real numbers B natural #’s A

8. The Symbols for numbers include: These can be used to write our solutions to equations in a funky way!

9. I digress….more on that later in the year. Two other important aspects of sets: 1. Union of sets: A B Symbol for Union or joining of sets is

10. 2. Intersection of sets C = {1, 3, 5, 7, 9, 11} D = {3, 6, 9, 12, 15} 3 6 9 12 15 18 1 3 5 7 9 11 1 5 3 7 9 11 6 12 15 18 C D

11. Definitions: Sets: are collections of clearly identified objects. Universal set is the collection of all objects under discussion. Subsets: part of the original set Complements of sets are elements of one set or the universal set but not included in the subset. A c or A' or ~A or means the complement of set A Union of sets is the combining of sets to form a new set. means union of sets A and B Intersection of sets is a set of all elements common to both sets. means intersection of sets A and B

12. The roster method has sets identified by capital letters. Each element of the set is listed between braces and separated by commas only. A set which has three ellipses on either end indicates the set continues in that direction.. Elements of sets are the individual things within a set. means 5 is an element of set A

13. Examples. Use the set of natural numbers for the following. The universal set: U is ______________________________________ 1. Write the set of numbers between 6 and 20 A: ________________________________________ 2. Write the set of natural numbers which are multiples of 5 Label it B. B:__________________________________________ 3. Write a set which is a complement of set B. Label it C. C: _________________________________________