Set Theory Operations in Maths

The symbol denotes the intersection operation. The set A B—also known as “A intersection B” or “A and B’s intersection”—is defined as the collection of all items that belong to both A and B. In the preceding example, the intersection of the two committees is the set of Blanshard and Hixon.

The idea of set operations is akin to the concept of fundamental operations on integers. In mathematics, a set is a finite collection of items, such as numbers, alphabets, or any other real-world objects. There are occasions when it is necessary to build a link between two or more sets. Then there’s the idea of set operations.

Set Operation

Set operations are used to combine items from two or more sets according to the operation done on them. A group of items is referred to as a set. Each item in a set is referred to as a ‘Element.’ There are three ways to represent a set. Statement form, roster form, and set builder notation are the three types. Set operations are actions that are performed on two or more sets in order to establish a connection between them. The following are the four primary types of set operations.

• Union of sets

• Intersection of sets

• Complement of a set

• Difference between sets/Relative Complement

Before we go over the various set operations, let’s review the notion of Venn diagrams, which is crucial to understanding set operations. A Venn diagram is a logical diagram that depicts the connection between two finite sets.

Union of sets (⋃)

A⋃B  is the set of distinct items that belong to set A and set B or both for two given sets A and B.

 n(A⋃B) = n(A) + n(B) -n(A⋂B), where n(X) is the number of elements in set X, gives the number of elements in A B. Considers the following example to better understand the set operation of the union of sets: If A = {1, 2, 3, 4} and B ={ 4, 5, 6, 7} then A⋃ B = {1, 2, 3, 4, 5, 6, 7 } is the A ⋃ B

The intersection of Sets (⋂)

A ⋂ B (read as A intersection B) is the set of common elements that belong to two given sets A and B. n(A⋂B) = n(A)+n(B)-n(A⋃B), where n(X) is the number of elements in set X, gives the number of elements in AB. Consider the following example to better understand the set operation of set intersection: A ⋂ B is given by A B = 3, 4 if A = 1, 2, 3, 4 and B = 3, 4, 5, 7.

Complement of Sets (A’)

The complement of a set A indicated as A′ or Ac, is the set of all items in the given universal set(U) that are not present in set A. Consider the following example to better understand the complement of sets set operation: If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {1, 2, 3, 4} then A’ = {5, 6, 7, 8, 9} is the A’.

Set Difference

A difference between sets is a set operation that involves removing members from a set, which is related to the idea of the difference between integers. All the items that are in set A but not in set B are listed in the difference between sets A and B, marked as A B. Consider the following example to better understand the set operation of set difference: If A ={ 1, 2, 3, 4 }and B = {3, 4, 5, 7 }then A – B ={ 1, 2} is the difference between sets A and B.

Set Operation formulas

Important Set Operation Notes

• The set operation formula for set union is n(A) + n(B) n(A⋃B), while the set operation formula for set intersection is n(A⋂B) = n(A)+n(B)n(A⋃B).

• Any set may be combined with the universal set to form the universal set, and any set A can be intersected with the universal set to form the set A.

• Set operations include union, intersection, difference, and complement.

• An empty set U′ = is the complement of a universal set. A universal set ′ = U is the complement of an empty set.

Uses of  Set Operations

• To connect the results of two SELECT operations, set operators are employed. UNION,UNION ALL, INTERSECT, and MINUS are the SET operators used.

• The combined results of the two SELECT queries are returned by the UNION set operator.

• It basically eliminates duplicates from the results, so for each duplicated result, only one row will be shown.

• To avoid this, use the UNION ALL set operator, which keeps duplicates in the final result.

• The MINUS set operator eliminates the second query’s results from the output if they are also found in the first query’s results.

Conclusion

Sets and subsets are pure mathematics fundamentals that lead to higher contemporary algebra. Instead of numerical or variable examples, you can use real-life examples for this topic. You may demonstrate how the symbols for belongs to, contained, and other common mathematical symbols work. Let’s take the classroom as an example, where a teacher and students are members of the classroom set, which is a subset of the school.

You can deduce that the sets apply to the entire universe. Sets are useful for logical and aptitude problems in general.