Step by step
The question
Question: find n(A × A), when A is {2, 4, 6, 8} and B is {1, 3}.
A = {2, 4, 6, 8}, 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.
n means how many.
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 Count the pairs
4 rows, 4 pairs in each row: 4 times 4 is 16.
Like counting choices: 4 ways for the first, 4 for the second.
n(A × A) = n(A) × n(A) = 4 × 4 = 16
3 Check
Let's check: the table has 16 cells, one pair each.
So it is right!
the table has 4 × 4 = 16 cells
Let's look back.
First: make the table.
Then: count the pairs.
Last: check.
Answer
n(A × A) = n(A) × n(A) = 4 × 4 = 16