Step by step
The question
Question: find n(A′ ∩ B), when ξ is the numbers 1 to 20, A is {1, 4, 9, 16} and B is {2, 4, 8, 16}.
ξ = {1, 2, …, 20}
A = {1, 4, 9, 16}
B = {2, 4, 8, 16}
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′ = not in A
n( ) = how many elements
n(A′ ∩ B) means: the elements not in A, and in B.
n means: how many elements.
n(A′ ∩ B) = = not in A, and in B
2 Draw the Venn diagram
3 Shade the part
n(A′ ∩ B) is not in A, and in B.
On the diagram: B only.
4 Read the answer
We count the shaded elements: 2, 8.
So n(A′ ∩ B) = 2.
n(A′ ∩ B) = 2
5 Check
Let's check some elements against the rule: not in A, and in B.
They fit.
So it is right!
2: not in A, in B; 8: not 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