Step by step
The question
Question: find A ∩ B, when ξ is the numbers 1 to 10, A is {2, 4, 6, 8} and B is {1, 2, 3, 4}.
ξ = {1, 2, …, 10}
A = {2, 4, 6, 8}
B = {1, 2, 3, 4}
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 both
A ∩ B means: the elements in A and in B: in both.
A ∩ B = = in A and in B: in both
2 Draw the Venn diagram
3 Shade the part
A ∩ B is in A and in B: in both.
On the diagram: the middle.
4 Read the answer
Careful!
Not every number from A and B.
Only the numbers that are in both.
Careful: only the elements in BOTH lists
The shaded part holds 2, 4.
We list them in order, each once.
A ∩ B = {2, 4}
5 Check
Let's check some elements against the rule: in A and in B: in both.
They fit.
So it is right!
2: in A, in B; 4: in A, in B
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 = {2, 4}