Set Definition
A set is an unordered collection of objects called elements.
Example:
The collection of a square, a circle, and a rectangle can be considered a set of the basic shapes. The square, circle, and rectangle are said to be elements of the set of basic shapes.
Point out all of the elements that do not belong in the set of dogs.
Roster Method
A set and its elements are often written in a shorthand form called the roster method. In this method, an uppercase letter is used to denote the set and all of the set's elements are listed between braces. For instance, the set of basic shapes can be denoted by:
S = {square, rectangle, circle}
Example 1:
The set of vowels can be denoted by:
V = {a, e, i, o, u}
Example 2:
The set of odd numbers from one to nine can be denoted by:
N = {1, 3, 5, 7, 9}
Match each set with its respective elements.

The set of even numbers from 2 to 10 ={2, 4, 6, 8, 10}

The set of cats ={cheeta, panther, lion}

The set of planets ={Venus, Mars, Jupiter, Saturn, Pluto}
Venn Diagrams
A Venn diagram is a graphical representation of a set. In a Venn diagram:
 A rectangle is used to represent all the objects under consideration, denoted by U (universal set)
 Inside the rectangle, circles are used to represent sets
 Points within the circles represent elements of the set
Example:
Suppose we want to construct a Venn diagram for the set of vowels. We can do so in the following steps:
 First we draw a rectangle to denote our universal set or U . This is the set of all objects under consideration, so in our case U is the 26 letters of the alphabet.
 Second, we draw a circle within the rectangle to represent the set of vowels, V.
 Lastly, we draw points within the circle to represent its individual elements. In our case, each point represents one of the five vowels.
Venn Diagram Construction
 N
 U
 1
 2
 3
 4
 5
Subsets
If we have a set A and a set B, then A is a subset of B if every element in A is also an element of B.
Example 1:
Suppose we have the following two sets:
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B = {1, 2, 3, 4, 5}
As we can see below, every element in B is also an element of A. Thus, B is a subset of A.
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B = {1, 2, 3, 4, 5}
Example 2:
Suppose we have the following two sets:
A = {a, b, c, d, e, f, g}
B = {1, 2, 3, 4, 5, 6, 7}
Because none of the elements in set B are in set A, B is not a subset of A.
Example 3:
Suppose we have the following two sets:
A = {1, 3, 5, 7, 9}
B = {1, 3, 4}
As we can see below, set A contains two of B's elements. However, set A does not contain the number 4 which is the third element of B. Thus, B is not a subset of A.
A = {1, 3, 5, 7, 9}
B = {1, 3, 4}
Identifying Subsets
Select the option below that is a subset of the set above.