Step by step
The question
Question: find A × B, when A is {a, b} and B is {1, 2, 3}.
A = {a, b}, B = {1, 2, 3}
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.
a with 1 is (a, 1).
2 List the pairs
We write the pairs row by row, inside curly brackets: (a, 1), (a, 2) and so on.
A × B = {(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)}
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 (1, a) in A × B ✗
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(A) × n(B) = 2 × 3
Let's look back.
First: make the table.
Then: list the pairs.
Last: check.
Answer
Careful: not (1, a) in A × B ✗