A = {1, 2, 3}, B = {6}, find A × B

Step by step

The question

Question: find A × B, when A is {1, 2, 3} and B is {6}.

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

A pair is written in round brackets.

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 6 is (1, 6).

2 List the pairs

We write the pairs row by row, inside curly brackets: (1, 6), (2, 6) and so on.

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 count: 3 pairs, and 3 times 1 is 3.

No pair twice.

So it is right!

Let's look back.

First: make the table.

Then: list the pairs.

Last: check.