Question:

Let A = {a, b}, B = {a, b, c}. Is \(\subset\) B? What is \(A ∪ B\)?

CBSE Class XI

Updated On: Jan 21, 2026

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Solution and Explanation

Here, A = {a, b} and B = {a, b, c}
Yes, \(A \subset B.\)
\(A \cup B\) = {a, b, c} = B

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Concepts Used:

Operations on Sets

Some important operations on sets include union, intersection, difference, and the complement of a set, a brief explanation of operations on sets is as follows:

1. Union of Sets:

The union of sets lists the elements in set A and set B or the elements in both set A and set B.
For example, {3,4} ∪ {1, 4} = {1, 3, 4}
It is denoted as “A U B”

2. Intersection of Sets:

Intersection of sets lists the common elements in set A and B.
For example, {3,4} ∪ {1, 4} = {4}
It is denoted as “A ∩ B”

3.Set Difference:

Set difference is the list of elements in set A which is not present in set B
For example, {3,4} - {1, 4} = {3}
It is denoted as “A - B”

4.Set Complement:

The set complement is the list of all elements present in the Universal set except the elements present in set A
It is denoted as “U-A”

Types of Sets

Sets are of various types depending on their features. They are as follows:

Empty Set - It is a set that has no element in it. It is also called a null or void set and is denoted by Φ or {}.
Singleton Set - It is a set that contains only one element.
Finite Set - A set that has a finite number of elements in it.
Infinite Set - A set that has an infinite number of elements in it.
Equal Set - Sets in which elements of one set are similar to elements of another set. The sequence of elements can be any but the same elements exist in both sets.
Sub Set - Set X will be a subset of Y if all the elements of set X are the same as the element of set Y.
Power Set - It is the collection of all subsets of a set X.
Universal Set - A basic set that has all the elements of other sets and forms the base for all other sets.
Disjoint Set - If there is no common element between two sets, i.e if there is no element of Set A present in Set B and vice versa, then they are called disjoint sets.
Overlapping Set - It is the set of two sets that have at least one common element, called overlapping sets.