## Complement of a set

Before studying about the Complement of s set, let us understand what sets are?

A well-defined collection of objects or elements is known as a set. Any set consisting of all the objects or elements related to a particular context is defined as a universal set. It is represented by \(U\)

For any set A which is a subset of the universal set \(U\)

To make it more clear consider a universal set \(U\)

Let the set \(A\)

Thus we can see that \(A\)

Now the complement of this set A consists of all those elements which is present in the universal set but not in \(A\)

\(A'\)

**Definition- Complement of a Set**

If \(U\)

\(A'\)

Alternatively it can be said that the difference of the universal set \(U\)

Let us now look into some examples to have a better insight.

**Example:** **Let \(U\) be the universal set which consists of all the integers greater than 5 but less than or equal to 25. Let \(A\) and \(B\) be the subsets of \(U\) defined as:**

**\(A\) = {\({x~:x~ âˆˆ~U ~and~ x~ is~ a~ perfect~ square}\)}**

**\(B\) = \({7, 9, 16, 18, 24}\)**

**Find the complement of sets A and B and the intersection of both the complemented sets.**

**Solution: **The universal set is defined as:

\(U\)

Also, \(A\)

\(B\)

The complement of set A is defined as:

\(A'\)

Therefore, \(A'\)

Similarly the complement of set B can be given by:

\(B'\)

The intersection of both the complemented sets is given by \(A’âˆ© B'\)

\(\Rightarrow A’âˆ© B'\)

We can see from the above discussions that if a set \(A\)

Now we are clear on the concept of complement of sets. There is a lot more to learn. Enrich your knowledge and reach new horizons of success by Downloading BYJUâ€™S the Learning App to know more or visit our website.

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