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Set operations are related to basic mathematical operations. In mathematics, a set is a finite collection of items, such as numbers, alphabets, or real-world objects. When the requirement to establish the relationship between two or more sets emerges, we must act quickly. Set operations are introduced at this point.
Set union, set intersection, set complement, and set difference are four of the most common set operations. We will discuss about union and intersection of the sets in maths in details.
Union of sets :-
One of the set operations used in set theory is the union of sets. Other set operations include difference and intersection, in addition to the union of sets. The unique operator is used to represent all set operations. Arithmetic addition is comparable to set union. The set that contains all of the elements in both sets is known as the union of two given sets.
The union of any two or more sets yields a fully new set that comprises a mixture of elements from both sets. The word ‘or’ is used to represent the union of sets. Consider the two sets A and B. All of the elements that are present in either A or B, or both sets, will be present in the union of A and B. The union of sets is represented by the set notation. The set operation, often known as the union of sets, is written as:
A U B = x: either x € A or x € B. x is the element that appears in both sets A and B.
Notation of union of sets :-
We use a unique mathematical notation to represent each set operation. The mathematical notation that is used to represent the union between two sets is ‘ U ’. This operator is called infix notation and it is surrounded by the operands.
Consider two sets P and Q, where P = { 1, 2, 3 } and Q = { 3, 4, 5 } then P U Q = { 1, 2, 3, 4, 5 }.
Properties of union of set :-
You’ll learn about some of the most essential properties of the union of sets in this section. When executing a set union, it is critical to take these qualities into account. Considering two sets A and B then
- Commutative property : A U B = B U A
- Associative property : ( A U B ) U C = A U ( B U C )
- Idempotent property : A U A = A
- Identity law : A U Ⲫ = A
- Universal set property : A U U = U
Intersection of sets :-
The set of elements that are shared by both sets is known as the intersection of sets. In set theory, the intersection is defined as the set of all the items in set A that are also present in set B for any two sets A and B. We use the sign for ‘intersection of’, which is “. Let’s use Brandon, Sophie, Luke, and Jess to represent students who enjoy ice cream for dessert. This is the first set. Ron, Sophie, Mia, and Luke are among the pupils that enjoy brownies as a dessert. This is the B set. Sophie and Luke are two classmates who enjoy both ice cream and brownies. This is denoted by the letters A and B.
Properties of intersection of sets :-
The qualities of intersection of sets are comparable to the properties of numbers. The commutative law, associative law, law of null set and universal set, and idempotent law are all properties of intersection of sets. The attributes of set intersection are listed below.
- Commutative property : A ∩ B = B ∩ A
- Associative property : ( A ∩ B ) ∩ C = A ∩ ( B ∩ C )
- Identity property : A ∩ A = A
- Law of U and Ⲫ : A ∩ Ⲫ = Ⲫ and A ∩ U = A
Conclusion :-
A collection of elements that belong to either A or B, or perhaps both, is defined as the union of two sets A and B. It’s simply described as the collection of all distinct elements or members that belong to one of these sets. The symbol ‘ U ’ for the union operator is, which stands for logical OR. A collection of elements that belong to both A and B is defined as the intersection of two sets A and B. It is simply defined as the set that contains all items of set A that are also members of set B, and vice versa. The logical AND is represented by the intersection operator.
