3.2.2 Real-World Applications

3.2.2 Real-World Applications

In this section, we will learn to apply concepts from set theory to real-world problems, such as solving problems on classification and cataloging using Venn diagrams. We will also explore some real-life situations, such as demographic classification and categorizing products in shopping malls.

For this purpose, we use the concept of cardinality of a set. The cardinality of a set is defined as the total number of elements of a set. The cardinality of a set is basically the size of the set. For a non-empty set $A$, the cardinality of a set is denoted by $n(A)$.

If $A = \{1, 3, 5, 7, 9, 11\}$, then $n(A) = 6$. To find the cardinality of a set, we use the following rule called the inclusion-exclusion principle for two or three sets.