Cartesian Product

The final part under the Sets section is Cartesian products. This is usually a small part but you may have 1 or 2 questions on the exam. The Cartesian product is basically every element in a set multiplied by every element in another Set. This creates a new set that contains paired elements. Sounds confusing doesn't it? Well I think an example will make it clear.

Example

Taking our sets to be:

A = {1,5,6}
B = {2,5,8}

Then the Cartesian product would be:

A x B ={(1,2),(1,5),(1,8),(5,2),(5,5),(5,8),(6,2),(6,5),(6,8)}

You can now see that we've taken every element in the first set and paired it with the element in the second set. If both sets have the same element, in this case 5, then you still pair them creating (5,5).

Practice Question

D = {1,6,9,10,15} E = {3,7,13,22}

Which of the following pairs is NOT an element in D x E ?

1. (6,13)
2. (9,7)
3. (10,15)
4. (1,22)

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