Sets 1st Year Mrs. Gilleran

What we will learn to do in this class:

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

Definition of A Set (Rules Copy)

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.

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.

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}

Symbols ∈ ∉

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

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

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}

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}

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

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}

What we learned in class today: