Disjoint Sets

Two sets A and B are called disjoint sets when they have no elements in common.

A simple way to recognize disjoint sets is to look at their intersection. If the intersection contains no elements, the two sets are disjoint. $$ A \cap B = \varnothing $$

A Practical Example

Consider the following sets:

$$ A = \{ 2,\ 4,\ 6,\ 8 \} $$

$$ B = \{ 1,\ 3,\ 5,\ 9 \} $$

Set A contains only even numbers, while set B contains only odd numbers.

Because a number cannot be both even and odd at the same time, the two sets have no elements in common.

In an Euler-Venn diagram, disjoint sets are shown as separate regions that do not overlap.

Since there are no common elements, the intersection of A and B is the empty set.

$$ A \cap B = \varnothing $$

Therefore, A and B are disjoint sets.

More generally, any two sets whose intersection is empty are called disjoint sets.