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

Step by step

The question

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

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.

2 with 1 is (2, 1).

2 Count the pairs

3 rows, 2 pairs in each row: 3 times 2 is 6.

Like counting choices: 3 ways for the first, 2 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 6 cells, one pair each.

So it is right!

Let's look back.

First: make the table.

Then: count the pairs.

Last: check.