1. Sets
1st Year
Mrs. Gilleran

2. What we will learn to do in this class:

3. Defining a Set Each of these collections is called a SET
The items in each of the collections is called the ELEMENTS of the set

4. Definition of A Set (Rules Copy)

5. We have to be clear which objects belong in a set and which do not.
“Write down the names of all of the tall people in the classroom.”
How could we make this clearer?
“Write down the names of all of the people in the class who are over 5 feet 6 inches in height.”
Whether someone is tall or not is an opinion. By including a measurement, our set is well-defined.

6. Which of these can be described as a well-defined Mathematics Set
The counties of Connaught
The players on my futsal team
The tall pupils in my class
The big towns in Ireland
Vowels
The best song in the charts at the moment.

7. Elements of a Set We name a set by a capital letter: A, B, C etc.
Elements: The objects which make up a set are called elements or members of the set.
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday W
We name a set by a capital letter: A, B, C etc.
The elements of a set are always placed within a set of curly (or chain) brackets. { }
What are the elements of the set W, the days of the week?
W = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

8. Symbols ∈ ∉

10. Describing a set
There are two ways:
The List Method
The Rule Method

11. The List Method Name the set with a capital letter.
Enclose the set in chain (curly) brackets {…}
Separate the elements with commas.
List each element only once.
The order in which you list the elements is not important

12. Example of List Method
List the elements that belong to the set: Months of the Year.
1. Name the set with a capital letter
A =
2. Put the elements inside curly brackets { }
A = {
3. Separate the elements with a comma
A = {Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec}

13. 2. The Rule Method Julie showed Reily the following set:
A = {2, 4, 6, 8, 10, 12}
How do you think Julie came up with the set?
A = {Spring, Summer, Autumn, Winter}
This set could also be wrote by using a rule to describe it
A = {Seasons of the Year}

14. A = {Days of Week Beginning with S} This can also be wrote as
A = {X | X is a day of the week beginning with the letter S} A Is
Of all elements, x,
Such that
The set
Each element, x, is a day of the week beginning with the letter S

16. The Null Set
If a set has no elements, then it is called the null set or the empty set.
∅ or { }
List the elements in the set D = {Days of the Week beginning with the letter P}

17. What we learned in class today: