Union of Sets: Overview, Questions, Preparation

The union of two sets, say set A & B is equal to the elements present in both the sets, and union of sets is the operation that focuses on collecting together the elements of both into a singular, third set. It should not be confused with a universal set, which is a set in itself. It is represented as - 

A ∪ B = {x:x ∈ A or a ∈ B}

A part of set theory, the union of two given sets, is defined as the smallest set containing all values of both sets. It is among the top 3 basic operations that can be performed on a set, alongside intersection and difference sets.

Similar to Mathematics, where people tend to perform the basic operations such as multiplication, division, subtraction, and addition, as part of the set theory, some basic operations are performed on two sets of values to give a common set of elements depending upon the operation performed. It is important to note that all elements are included in the set when it comes to the union.

Venn Diagram: Representing Union of Sets 

In order to represent the union of sets, you can use a Venn diagram. Let us consider that for a universal set X. We have two sets, A and B, which are subsets of the universal set X, whose union would be a combination of all the elements in the set A and B altogether, represented by the symbol ∪.

Union of Sets: Properties 

There are 5 main properties related to the union of sets, which are listed below - 

Commutative Law: As per commutative law, the union of sets will follow commutative law when - A∪B=B∪A

Associative Law: When we have 3 sets, associative law states that - (A∪B)∪C = A∪(B∪C)

Identity Law: Union of an empty set with a set A will result in A∪∅=A

Idempotence Law: Union of a set with itself will result in the set itself, implying - A∪A=A

Domination Law:  the union of universal set X with a subset P will give the universal set a result equal to itself; represented by -X ∪ P= X

Importance and Weightage

This topic is covered under the ‘Sets’ chapter in the Class 11th Mathematics syllabus. Here you’ll learn about the union of sets and intersection, empty sets & their representation using Venn diagrams. 

The chapter contributes 23 marks to the question paper in terms of weightage & must be prepared well. 

1.  A = {4,3,5} & B = {6,8,7}; represent union of sets using a venn diagram. 

Solution. A∪B = {3,4,5, 6,7,8} 

2. When P = {3, 5, 8} & Q = {4, 9, 2}, find P∪Q. 

Solution. P∪Q = {3,5,8,4,9,2} 

3. When M = {a, d, e} & N = {b, c,f}, represent M ∪ N, using a venn diagram. 

Solution. M∪ N = {a,d,e, b,c,f}

Q: What are sets?

Q: What is the cardinal number of a set?

Q: What is a Venn diagram?

Q: What is the complement of a set?

Q: What is the intersection of sets?