Difference of sets
This lesson will explain how to find the difference of sets. We will start with a definition
Definition:
Given set A and set B the set difference of set B from set A is the set of all element in A, but not in B.
We can write A − B
Example #1.
Take a close look at the figure above. Elements in A
only are b, d, e,g.
Therefore, A − B = { b, d, e, g}
Notice that although elements a, f, c are in A, we did not include them in A − B because we must not take anything in set B.
Sometimes, instead of looking at a the Venn Diagrams, it may be easier to write down the elements of both sets
Then, we show in bold the elements that are in A, but not in B
A = {
b,
d,
e,
g, a, f, c}
B = { k, h, u, a, f, c}
Example #2.
Find B − A
Notice that this time you are looking for anything you see in B
only
Elements that are in B only are shown in bold below
Let A = {1 orange, 1 pinapple, 1 banana, 1 apple}
Let B = {1 orange,
1 apricot, 1 pinapple, 1 banana,
1 mango, 1 apple,
1 kiwifruit }
B − A = {1 apricot, 1 mango, 1 kiwifruit}
Example #3.
Find A − B
B = { 1, 2, 4, 6}
A = {1, 2, 4, 6,
7,
8,
9 }
What I see in A that are not in B are 7, 8, and 9
A − B = { 7, 8, 9}
Example #4.
Find B − A
A = { x / x is a number bigger than 6 and smaller than 10}
B = { x / x is a positive number smaller than 15}
A = {7, 8, 9} and B = {
1,
2,
3,
4,
5,
6, 7, 8, 9,
10,
11,
12,
13,
14}
Everything you see in bold above are in B only.
B − A = {1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14}
The graph below shows the shaded region for A − B and B − A
This ends the lesson about the difference of sets.
Difference of sets quiz to see how well you understand this lesson.

Jul 28, 17 02:38 PM
Bessy has 6 times as much money as Bob, but when each earn $6. Bessy will have 3 times as much money as Bob. How much does each have before and after
Read More
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.