A = {p, q}, B = {1, 2}, find B × A

Step by step

The question

Question: find B × A, when A is {p, q} and B is {1, 2}.

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

A pair is written in round brackets.

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 p is (1, p).

2 List the pairs

We write the pairs row by row, inside curly brackets: (1, p), (1, q) and so on.

Careful!

The order matters.

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

So B × A is not the same as A × B.

3 Check

Let's check the count: 4 pairs, and 2 times 2 is 4.

No pair twice.

So it is right!

Let's look back.

First: make the table.

Then: list the pairs.

Last: check.