While we have discussed union, intersections, and complements of two or more sets, one often forgotten component of set theory is the case where two sets are disjoint. Two sets A and B are called disjoint if A and B have no elements in common. Another equivalent definition of disjoint sets would be that the intersection of the two sets actually equals the empty set. While we can debate which definition has a nicer ring to it, the main focus here is to be able to identify when two sets are disjoint.
Examples of Disjoint Sets
In all of the above examples notice that none of the two sets listed on a single line share an element. As a result, each case provides us with an example of disjoint sets. While this may seem like an easy task, it can be harder to check as the cardinality of our sets increase.
Examples of Sets that are not Disjoint
Depending upon our familiarity with certain topics, these examples can range from an easy solution to a more difficult one, depending upon our familiarity with the topic. We shall explain why the above sets are not disjoint here.
Reasons the Above Sets are not Disjoint
In order to further comprehend the material, please attempt the following exercises.