Step by step
The question
Question: find n(B × A), when A is {5, 6} and B is {1, 2, 3, 4}.
A = {5, 6}, B = {1, 2, 3, 4}
B × A means: every pair with the first number from B and the second from A.
A pair is written in round brackets.
n means how many.
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 5 is (1, 5).
2 Count the pairs
4 rows, 2 pairs in each row: 4 times 2 is 8.
Like counting choices: 4 ways for the first, 2 for the second.
n(B × A) = n(B) × n(A) = 4 × 2 = 8
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 (5, 1) in B × A ✗
3 Check
Let's check: the table has 8 cells, one pair each.
So it is right!
the table has 4 × 2 = 8 cells
Let's look back.
First: make the table.
Then: count the pairs.
Last: check.
Answer
Careful: not (5, 1) in B × A ✗