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.
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