Step by step
The question
Question: find n(A ∩ B), when ξ is the numbers 1 to 12, A is {3, 6, 9, 12} and B is {2, 4, 6, 8, 10, 12}.
ξ = {1, 2, …, 12}
A = {3, 6, 9, 12}
B = {2, 4, 6, 8, 10, 12}
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
n( ) = how many elements
n(A ∩ B) means: the elements in A and in B: in both.
n means: how many elements.
n(A ∩ B) = = in A and in B: in both
2 Draw the Venn diagram
3 Shade the part
n(A ∩ B) is in A and in B: in both.
On the diagram: the middle.
4 Read the answer
We count the shaded elements: 6, 12.
So n(A ∩ B) = 2.
n(A ∩ B) = 2
5 Check
Let's check some elements against the rule: in A and in B: in both.
They fit.
So it is right!
6: in A, in B; 12: 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
n(A ∩ B) = 2