Step by step
The question
Question: find A × A, when A is {2, 4} and B is {1, 3}.
A = {2, 4}, B = {1, 3}
A × A means: every pair with the first number from A and the second from A.
A pair is written in round brackets.
A × A = every pair (first from A, second from A)
1 Make the table
Across the top: the elements of A.
Down the side: the elements of A.
Each cell is a pair: its row first, its column second.
2 with 2 is (2, 2).
2 List the pairs
We write the pairs row by row, inside curly brackets: (2, 2), (2, 4) and so on.
A × A = {(2, 2), (2, 4), (4, 2), (4, 4)}
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(A) = 2 × 2
Let's look back.
First: make the table.
Then: list the pairs.
Last: check.
Answer
A × A = {(2, 2), (2, 4), (4, 2), (4, 4)}