Introduction to set theory with Python. Part II.

Topics: Set difference, complement of a set.

On this post, we are talking about some other topics we didn´t covered on the previous one.

https://dev.to/eaarroyo/introduction-to-set-theory-with-python-3jol

Let's start with set difference.

Set Difference

The difference of two sets is writter as:

A \ B or A - B.

If A = {1, 2, 3} and B = {3, 4, 5}, the difference is a set of those objects of A that are not in B.

e.g. A - B = {1, 2}

In builder notation this would be:

A\B = {x : x ∈ A and x ∉ B };

#Python Script
A = {1, 2, 3}
B = {3, 4, 5}

A.difference(B) #  Output is {1, 2}

Complement of a set

The complement of a set are all those elements of the universal set that are not on the other set.

So, for this, we need to define a Universal set such as:

U = {1, 2, 3, 4}

A = {2, 3}

A' = {1, 4}

A' is the complement of A. Being U the universal set.

It can be written in builder notation like this:

A' = {x ∈ U and x ∉ A };

This present to us something really interesting:

Being:

U = {1, 2, 3, 4}

A = {2, 3}

U - A = {x : x ∈ U and x ∉ A };

U - A = {1, 4}

And,

A' = {x ∈ U and x ∉ A };

A' = {1, 4}

So, A' = U - A;

In python there is not a "Complement of a set" method, per se. So this would need to be done with the difference method.

#Python script
U = {1, 2, 3, 4}
A = {2, 3}

U.difference(A) # Output: {1, 4}

Written by E. A. Arroyo