How to Find the Complement of a Set?

The complement of a set is simply found by excluding the elements of the given set from the universal set. This is shown in the example below.

Example: Find the complement of set S = {4, 8, 12, 16}, where the universal set is all multiples of 4 that are smaller than 50.

Solution:

Step 1: Identify the universal set (U) and the set (S) for which you want to find the complement.

Universal Set(U) = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}

Also, given: S = {4, 8, 12, 16}

Step 2: Calculate the complement of set S by excluding the elements of S from the universal set U i.e., S’ = U – S.

S’ = U – S = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48} – {4, 8, 12, 16}

Step 3: Simplify the resulting set to obtain the complement.

Thus, S’ = {20, 24, 28, 32, 36, 40, 44, 48}

Complement of a Set is one of the important operations, we can perform on a set in set theory. Grouping numbers with similar properties together, i.e., arranging them in sets is what forms the foundation for the rest of mathematics, thus set theory holds a very important place in the study of mathematics.

Having learned the importance of set theory, it is important to go through all its aspects to fully grasp its concept. In this article, we will learn about a particular aspect of set theory: complement of a set: its meaning, symbol, properties, and Venn diagram.