0.4. Cartesian product
We know we can use binary operations to add two numbers, x and y: Furthermore there are other operations such as or any other root and exponents. Operations can involve other mathematical objects other than numbers, such as sets.
Given two sets, A and B, we can define multiplication of these two sets as the Cartesian product. The new set is defined as
Before looking at abstract examples, consider this case:
e.g.1. Assume there is a student in a self-catering residence and they want to make food preps for the first four days in the week. They want to know how many possible combinations they can make using fruits (between grapes and apples) and meals (pasta and meatballs, chicken wrap).
To solve this, let
Then the possible meal options are: (grapes, pasta and meatballs), (grapes, chicken wrap), (apples, pasta and meat balls) and (apples, chicken wrap).
The Cartesian Product of sets A and B would be:
We can think of the above example in more abstract terms.…