Properties of Complement of a Set – Explanation, Types, Solved Example, and FAQs

# Properties of Complement of a Set – Explanation, Types, Solved Example, and FAQs

## What is a Set?

A set is a collection of objects. It can be any collection of objects, including numbers, letters, words, or other items.

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## What are the Types of Sets?

There are three types of sets: finite sets, infinite sets, and null sets.

1. A finite set is a set that has a finite number of members.
2. An infinite set is a set that has an infinite number of members.
3. A null set is a set that has no members.

## Properties of Complement of Set

The complement of a set is the set of all elements that are not in the original set. The complement is written as the set’s symbol followed by a caret (^), for example, the complement of the set {1, 2, 3} is the set {4, 5, 6}.

The complement of a set is always a subset of the set’s universal set. In other words, the complement of a set always includes all of the elements in the universal set that are not in the original set.

The complement of a set is also always a subset of the set’s intersection. This means that if you intersect the original set with its complement, the result will be the original set.

Finally, the cardinality of the complement of a set is always equal to the cardinality of the original set minus 1.

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