Step by step
The question
Question: find A ∪ B, when ξ is the numbers 10 to 20, A is {12, 14, 16, 18, 20} and B is {15, 20}.
ξ = {10, 11, …, 20}
A = {12, 14, 16, 18, 20}
B = {15, 20}
1 Read the sets
A set is a list of numbers in curly brackets.
Each number is an element.
ξ is the set of everything we look at.
ξ = everything we look at
∪ = in A or in B (or both)
A ∪ B means: the elements in A or in B, or in both.
A ∪ B = = in A or in B, or in both
2 Draw the Venn diagram
3 Shade the part
A ∪ B is in A or in B, or in both.
On the diagram: A only, the middle, B only.
4 Read the answer
Careful!
20 is in both sets.
In a set, each element is written once.
Careful: not {12, 14, 16, 18, 20, 15, 20} ✗
The shaded part holds 12, 14, 15, 16, 18, 20.
We list them in order, each once.
A ∪ B = {12, 14, 15, 16, 18, 20}
5 Check
Let's check by counting.
A has 5, B has 2, and 1 were counted twice.
5 plus 2 minus 1 is 6: the same count.
So it is right!
n(A) + n(B) − n(A ∩ B) = 5 + 2 − 1 = 6
Let's look back.
First: read the sets.
Then: draw the Venn diagram.
Then: shade the part.
Then: read the answer.
Last: check.
Answer
A ∪ B = {12, 14, 15, 16, 18, 20}