Step by step
The question
Question: find A × B, when A is {2, 3} and B is {4, 5}.
A = {2, 3}, B = {4, 5}
A × B means: every pair with the first number from A and the second from B.
A pair is written in round brackets.
A × B = every pair (first from A, second from B)
1 Make the table
Across the top: the elements of B.
Down the side: the elements of A.
Each cell is a pair: its row first, its column second.
2 with 4 is (2, 4).
2 List the pairs
We write the pairs row by row, inside curly brackets: (2, 4), (2, 5) and so on.
A × B = {(2, 4), (2, 5), (3, 4), (3, 5)}
Careful!
The order matters.
In A × B the first number always comes from A.
So A × B is not the same as B × A.
Careful: not (4, 2) in A × B ✗
3 Check
Let's check the count: 4 pairs, and 2 times 2 is 4.
No pair twice.
So it is right!
4 pairs = n(A) × n(B) = 2 × 2
Let's look back.
First: make the table.
Then: list the pairs.
Last: check.
Answer
Careful: not (4, 2) in A × B ✗