List the elements of A ∩ B. Step by Step

Step by step

The question

Question: find A ∩ B, when ξ is the numbers 1 to 12, A is {2, 4, 6, 8, 10, 12} and B is {3, 6, 9, 12}.

ξ = {1, 2, …, 12}

A = {2, 4, 6, 8, 10, 12}

B = {3, 6, 9, 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

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

The box is ξ: every element goes somewhere in it.

First the middle: 6, 12 are in A and in B.

Then the rest of A: 2, 4, 8, 10.

Then the rest of B: 3, 9.

What is in neither goes outside the circles: 1, 5, 7, 11.

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 6, 12.

We list them in order, each once.

A ∩ B = {6, 12}

5 Check

Let's check 6 and 12 against the rule: in A and in B: in both.

6 is in A, and it is in B.

12 is in A, and it is in B.

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