A = {1, 2, 3, 4}, B = {5, 6, 7}, find n(A × B)

Step by step

The question

Question: find n(A × B), when A is {1, 2, 3, 4} and B is {5, 6, 7}.

A × B means: every pair with the first number from A and the second from B.

A pair is written in round brackets.

n means how many.

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.

1 with 5 is (1, 5).

2 Count the pairs

4 rows, 3 pairs in each row: 4 times 3 is 12.

Like counting choices: 4 ways for the first, 3 for the second.

Careful!

The order matters.

In A × B the first number always comes from A.

So A × B is not the same as B × A.

3 Check

Let's check: the table has 12 cells, one pair each.

So it is right!

Let's look back.

First: make the table.

Then: count the pairs.

Last: check.