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 \(A\)
Definition- Complement of a Set
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 \(U\)
Find the complement of sets A and B and the intersection of both the complemented sets.
Solution: The universal set is defined as:
The complement of set A is defined as:
Similarly the complement of set B can be given by:
The intersection of both the complemented sets is given by \(A’∩ B’\)
\(\Rightarrow A’∩ B’\)
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 BYJU’S the Learning App to know more or visit our website.
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