Disjoint Sets

In the set theory, we term two sets as disjoint sets when they have no elements in common. In other words, the intersection of these two sets results in an empty set, which is represented as $$ A ∩ B = ∅ $$

Let's explore this with a real-world example.

Take these two sets:

$$ A = {1, 2, 3, 4} $$

$$ B = {5, 6, 7} $$

It's clear that sets A and B don't share any common elements.

Consequently, we classify A and B as disjoint sets.

Should you attempt to depict sets A and B using Venn diagrams, you'd find that disjoint sets do not overlap—they share no common area.

Interestingly, disjointness possesses a commutative property. This means that if A and B are disjoint, then the same applies for B and A. Essentially, the order in which sets are presented doesn't influence the property of disjointness.

For further clarity, consider this additional example.

Take the following sets:

$$ A = {1, 2, 3} $$

$$ B = {4, 5, 6} $$

$$ C = {3, 7, 8} $$

In this context, A is disjoint with B, but not with C—sets A and C have the common element of 3.

Furthermore, sets B and C are deemed disjoint, as they do not share any common elements.