Step by step
The question
Question: find B × A, when A is {0, 2} and B is {1, 2, 3}.
A = {0, 2}, B = {1, 2, 3}
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.
1 with 0 is (1, 0).
2 List the pairs
We write the pairs row by row, inside curly brackets: (1, 0), (1, 2) and so on.
B × A = {(1, 0), (1, 2), (2, 0), (2, 2), (3, 0), (3, 2)}
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 (0, 1) in B × A ✗
3 Check
Let's check the count: 6 pairs, and 3 times 2 is 6.
No pair twice.
So it is right!
6 pairs = n(B) × n(A) = 3 × 2
Let's look back.
First: make the table.
Then: list the pairs.
Last: check.
Answer
Careful: not (0, 1) in B × A ✗