Basic Set Notation
Problem 1: Mrs. Glosser asked Kyesha, Angie and Eduardo to join the new math club. After school they signed up and became members. They wrote about it on the chalkboard using set notation:
P = {Kyesha, Angie and Eduardo}
When Angie’s mother came to pick her up, she looked at the chalkboard and asked: What does that mean?
Solution: Let P be the set of all members in the math club.
An object that belongs to a set is called an element (or a member) of that set. We use special notation to indicate whether or not an element belongs to a set, as shown below.
Symbol | Meaning |
is an element of | |
is not an element of |
For example, given the set A = {1, 2, 3, 4, 5}, we can write 1 A, which stands for 1 is an element of set A. We can also write 7 A, which stands for 7 is not an element of set A. Let’s look at some more examples of this.
Set | Notation | Meaning |
A = {2, 4, 6, 8} | 2 A | 2 is an element of A |
5 A | 5 is not an element of A | |
B = {a, e, i, o, u} | e B | e is an element of B |
w B | w is not an element of B | |
C = {1, 3, 5, 7, 9} | 7 C | 7 is an element of C |
2 C | 2 is not an element of C | |
D = {-3, -2, -1, 0, 1, 2, 3} | -2 is an element of D | |
One-half is not an element of D |
Determine if the given item is an element of the set. | ||
Set | Item | Is an element? |
R = {2, 4, 6, 8} | 10 | |
S = {2, 4, 6, 8, 10} | 10 | |
D = {English alphabet} | m | |
D = {English alphabet} | ||
X = {prime numbers less than 10} | 9 | |
A = {even numbers} | 8 |
Summary: An object that belongs to a set is called an element (or a member) of that set. We use special notation to indicate whether or not an element belongs to a set: (),
Exercises
Directions: Read each question below. Select your answer by clicking on its button. Feedback to your answer is provided in the RESULTS BOX. If you make a mistake, rethink your answer, then choose a different button.
1. | Which of the following is a true statement for set R? R = {liquid, gas, solid, plasma} |
2. | Which of the following is true for set G?G = {1, 3, 5, 7, 9} |
3. | Which of the following statements is true about set B?B = {US flag colors} |
4. | Which of the following elements is not a member of set X? X = {tiger, lion, puma, cheetah, leopard, cougar, ocelot} |
5. | Which of the following elements is not a member of set A?A = {states in the US} |