# 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} gas  R  solid  R  liquid  R  None of the above.RESULTS BOX:
 2. Which of the following is true for set G?G = {1, 3, 5, 7, 9} 5   G  7  G  3  G  All of the above.RESULTS BOX:
 3. Which of the following statements is true about set B?B = {US flag colors} red  B  blue  B  white  B  All of the above.RESULTS BOX:
 4. Which of the following elements is not a member of set X? X = {tiger, lion, puma, cheetah, leopard, cougar, ocelot} cougar  bobcat  puma  tigerRESULTS BOX:
 5. Which of the following elements is not a member of set A?A = {states in the US} Guam  Haiti  Philippines  All of the above.RESULTS BOX: