Step by step
The question
Question: find B × A, when A is {1, 2, 3} and B is {4, 5}.
A = {1, 2, 3}, B = {4, 5}
B × A means: every pair with the first number from B and the second from A.
A pair is written in round brackets.
B × A = every pair (first from B, second from A)
1 Make the table
Across the top: the elements of A.
Down the side: the elements of B.
Each cell is a pair: its row first, its column second.
4 with 1 is (4, 1).
2 List the pairs
We write the pairs row by row, inside curly brackets: (4, 1), (4, 2) and so on.
B × A = {(4, 1), (4, 2), (4, 3), (5, 1), (5, 2), (5, 3)}
Careful!
The order matters.
In B × A the first number always comes from B.
So B × A is not the same as A × B.
Careful: not (1, 4) in B × A ✗
3 Check
Let's check the count: 6 pairs, and 2 times 3 is 6.
No pair twice.
So it is right!
6 pairs = n(B) × n(A) = 2 × 3
Let's look back.
First: make the table.
Then: list the pairs.
Last: check.
Answer
Careful: not (1, 4) in B × A ✗