Basic Set Notation

Group WorkProblem 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_0.gif is an element of
is_not_an_element_of_1.gif is not an element of

For example, given the set A = {1, 2, 3, 4, 5}, we can write 1 is_an_element_of_0.gif A, which stands for 1 is an element of set A. We can also write 7 is_not_an_element_of_1.gif 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} is_an_element_of_0.gif A 2 is an element of A
  is_not_an_element_of_1.gif A 5 is not an element of A
B = {a, e, i, o, u} is_an_element_of_0.gif B e is an element of B
  is_not_an_element_of_1.gif B w is not an element of B
C = {1, 3, 5, 7, 9} is_an_element_of_0.gif C 7 is an element of C
  is_not_an_element_of_1.gif C 2 is not an element of C
D = {-3, -2, -1, 0, 1, 2, 3} negative2_is_element_of_d.gif -2 is an element of D
  1over2_not-elenent_of_d.gif 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 10_not-element_r_red.gif
S = {2, 4, 6, 8, 10} 10 10_is-element_s_red.gif
D = {English alphabet} m
D = {English alphabet} sigma.gif sigma_not-element_d_red.gif
X = {prime numbers less than 10} 9 9-not-element_x_red.gif
A = {even numbers} 8 8-is-element_a_red.gif

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: (element_and_not_an_element.gif),


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 is_not_an_element_of_transparent.gif R
 solid is_not_an_element_of_transparent.gif R
 liquid is_an_element_of_transparent.gif R
 None of the above.

RESULTS BOX:
 

2. Which of the following is true for set G?

G = {1, 3, 5, 7, 9}


 
 
 5  is_not_an_element_of_transparent.gif G
 7 is_an_element_of_transparent.gif G
 3 is_not_an_element_of_transparent.gif G
 All of the above.

RESULTS BOX:
 

3. Which of the following statements is true about set B?

B = {US flag colors}


 
 
 red is_an_element_of_transparent.gif B
 blue is_an_element_of_transparent.gif B
 white is_an_element_of_transparent.gif 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
 tiger

RESULTS 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:
 

IXL