Union vs. Intersection — What's the Difference?
By Tayyaba Rehman — Updated on October 30, 2023
In set theory, the union of two sets contains all elements from both sets, without duplicates. It represents the total of all unique members from those sets. The Intersection of two sets includes only those elements that are common to both sets.
Difference Between Union and Intersection
Table of Contents
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Key Differences
In set theory, the union of two sets contains all elements from both sets, without duplicates. It represents the total of all unique members from those sets. On the other hand, the intersection of two sets includes only those elements that are common to both sets, effectively highlighting the overlap between them.
A union merges different groups, emphasizing inclusivity. It’s like gathering different fruits into one basket, ending up with a variety of types. The intersection is the selective process, akin to choosing only the fruits that appear more than once in multiple baskets, focusing on commonality.
When you create a union of A and B, every element from A and every element from B is represented. For example, in a union of two circles in a Venn diagram, the area of the union encompasses the entire space of both circles. The intersection, however, would be represented only by the overlapping area where both circles cover the same space.
Unions are used when the goal is to combine resources, information, or elements, providing a comprehensive collection. Intersections are utilized when the aim is to find similarities or to filter through two sets for matching elements. Both are foundational concepts in mathematics, logic, and data analysis.
The concept of union extends beyond mathematics to political and social contexts, implying the act of joining or uniting groups. Intersection can also have broader meanings, including the point where two different paths or ideas meet, often used in geography and discussions of social issues.
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Comparison Chart
Definition
Combination of all elements from sets
Common elements between sets
Symbol
∪
∩
Set Theory Result
Larger or equal set than individual sets
Smaller or equal set than individual sets
Venn Diagram
Overlapping and non-overlapping areas
Only the overlapping area
Example
A∪B={1,2,3,4,5}
A∩B={3,4}
Compare with Definitions
Union
The act of joining two or more groups
The union of the two companies was announced yesterday.
Intersection
A point where two or more things cross
The intersection of the two roads was busy.
Union
The state of being united or joined
In marriage, they found the union of their dreams.
Intersection
The act of intersecting
The intersection of their ideas sparked a new theory.
Union
The act of uniting or the state of being united.
Intersection
A crossroad or junction
He stood at the busy intersection, undecided.
Union
A combination so formed, especially an alliance or confederation of people, parties, or political entities for mutual interest or benefit.
Intersection
In mathematics, the intersection of two or more objects is another, usually "smaller" object. Intuitively, the intersection of objects is that which belongs to all of them.
Union
(Mathematics) A set, every member of which is an element of one or another of two or more given sets.
Intersection
The act, process, or result of intersecting.
Union
Agreement or harmony resulting from the uniting of individuals; concord.
Intersection
A place where things intersect, especially a place where two or more roads cross.
Union
The state of matrimony; marriage
"The element that was to make possible such a union was trust in each other's love" (Kate Chopin).
Intersection
The point or locus of points where one line, surface, or solid crosses another.
Union
Sexual intercourse.
Intersection
A set that contains elements shared by two or more given sets.
Union
A combination of parishes for joint administration of relief for the poor in Great Britain.
Intersection
The junction of two (or more) paths, streets, highways, or other thoroughfares.
Union
A workhouse maintained by such a union.
Intersection
Any overlap, confluence, or crossover.
Union
A labor union.
Intersection
(geometry) The point or set of points common to two geometrical objects (such as the point where two lines meet or the line where two planes intersect).
Union
A coupling device for connecting parts, such as pipes or rods.
Intersection
(set theory) The set containing all the elements that are common to two or more sets.
Union
A device on a flag or ensign, occupying the upper inner corner or the entire field, that signifies the union of two or more sovereignties.
Intersection
(sports) The element where two or more straight lines of synchronized skaters pass through each other.[http://www.isu.org/vsite/vcontent/content/transnews/0,10869,4844-128590-19728-18885-295370-3787-4771-layout160-129898-news-item,00.html]
Union
An organization at a college or university that provides facilities for recreation; a student union.
Intersection
(category theory) The pullback of a corner of monics.
Union
A building housing such facilities.
Intersection
The act, state, or place of intersecting.
Union
Union The United States of America regarded as a national unit, especially during the Civil War.
Intersection
The point or line in which one line or surface cuts another.
Union
Union Of, relating to, or loyal to the United States of America during the Civil War
A Union soldier.
Intersection
A point where lines intersect
Union
Of or relating to a labor union or labor union organizing
The union movement.
Union negotiations.
Intersection
A junction where one street or road crosses another
Union
(countable) The act of uniting or joining two or more things into one.
Intersection
A point or set of points common to two or more geometric configurations
Union
(countable) The state of being united or joined; a state of unity or harmony.
Intersection
The set of elements common to two or more sets;
The set of red hats is the intersection of the set of hats and the set of red things
Union
(countable) That which is united, or made one; something formed by a combination or coalition of parts or members; a confederation; a consolidated body; a league.
Intersection
A representation of common ground between theories or phenomena;
There was no overlap between their proposals
Union
(countable) A trade union; a workers' union.
Intersection
The act of intersecting (as joining by causing your path to intersect your target's path)
Union
(countable) An association of students at a university for social and/or political purposes; also in some cases a debating body.
Intersection
The set of common elements in sets
The intersection of the circles is small.
Union
(countable) A joint or other connection uniting parts of machinery, such as pipes.
Intersection
Where different areas or concepts meet
Her interests lie at the intersection of science and art.
Union
The set containing all of the elements of two or more sets.
Union
(countable) The act or state of marriage.
Union
Sexual intercourse.
Union
A data structure that can store any of various types of item, but only one at a time.
Union
A large, high-quality pearl.
Union
(historical) An affiliation of several parishes for joint support and management of their poor; also the jointly-owned workhouse.
Union
To combine sets using the union operation.
Union
Belonging to, represented by, or otherwise pertaining to a labour union.
Actors have to be union to get work here.
Union
The act of uniting or joining two or more things into one, or the state of being united or joined; junction; coalition; combination.
Union
Agreement and conjunction of mind, spirit, will, affections, or the like; harmony; concord.
Union
That which is united, or made one; something formed by a combination or coalition of parts or members; a confederation; a consolidated body; a league; as, the weavers have formed a union; trades unions have become very numerous; the United States of America are often called the Union.
Union
A textile fabric composed of two or more materials, as cotton, silk, wool, etc., woven together.
Union
A large, fine pearl.
If they [pearls] be white, great, round, smooth, and weighty . . . our dainties and delicates here at Rome . . . call them unions, as a man would say "singular," and by themselves alone.
In the cup an union shall he throw,Richer than that which four successive kingsIn Denmark's crown have worn.
Union
A device emblematic of union, used on a national flag or ensign, sometimes, as in the military standard of Great Britain, covering the whole field; sometimes, as in the flag of the United States, and the English naval and marine flag, occupying the upper inner corner, the rest of the flag being called the fly. Also, a flag having such a device; especially, the flag of Great Britain.
Union
A joint or other connection uniting parts of machinery, or the like, as the elastic pipe of a tender connecting it with the feed pipe of a locomotive engine; especially, a pipe fitting for connecting pipes, or pipes and fittings, in such a way as to facilitate disconnection.
Union
A cask suspended on trunnions, in which fermentation is carried on.
One kingdom, joy, and union without end.
[Man] is to . . . begetLike of his like, his image multiplied.In unity defective; which requiresCollateral love, and dearest amity.
Union
An organization of employees formed to bargain with the employer;
You have to join the union in order to get a job
Union
The United States (especially the northern states during the American Civil War);
He has visited every state in the Union
Lee hoped to detach Maryland from the Union
The North's superior resources turned the scale
Union
The act of pairing a male and female for reproductive purposes;
The casual couplings of adolescents
The mating of some species occurs only in the spring
Union
The state of being joined or united or linked;
There is strength in union
Union
The state of being a married couple voluntarily joined for life (or until divorce);
A long and happy marriage
God bless this union
Union
Healing process involving the growing together of the edges of a wound or the growing together of broken bones
Union
A political unit formed from previously independent people or organizations;
The Soviet Union
Union
A set containing all and only the members of two or more given sets;
Let C be the union of the sets A and B
Union
The occurrence of a uniting of separate parts;
Lightning produced an unusual union of the metals
Union
A device on a national flag emblematic of the union of two or more sovereignties (typically in the upper inner corner)
Union
The act of making or becoming a single unit;
The union of opposing factions
He looked forward to the unification of his family for the holidays
Union
Being of or having to do with the northern United States and those loyal to the Union during the Civil War;
Union soldiers
Federal forces
A Federal infantryman
Union
Of trade unions;
The union movement
Union negotiations
A union-shop clause in the contract
Union
A group of workers collectively bargaining
The workers formed a union for better wages.
Union
A political unit constituting an entity
The European Union is an economic and political union.
Union
The set containing all distinct elements
The union of the two sets includes all their elements.
Common Curiosities
How is the intersection symbol represented?
The intersection is represented by the symbol ∩.
How is the union symbol represented?
The union is represented by the symbol ∪.
Can the union of sets be empty?
No, the union of sets cannot be empty as it contains at least all the elements of the individual sets.
Is the intersection of a set with itself just the set?
Yes, the intersection of a set with itself is the set itself.
What is a union in mathematics?
It's the set of all unique elements present in any of the given sets.
What is an intersection in mathematics?
It's the set of elements that are common to all given sets.
Is the union of a set with itself just the set?
Yes, the union of a set with itself is the set itself.
What does a union represent in politics?
In politics, a union typically refers to the formation of a single political entity from multiple territories or states.
Can a union be part of another union?
Yes, unions can be nested or part of larger unions.
Can the intersection of sets be empty?
Yes, the intersection can be empty if there are no common elements between the sets.
Are union and intersection mutually exclusive in math?
No, they are not mutually exclusive; they are different operations on sets.
What is the intersectionality theory?
It's a theory that explores how different social identities overlap and how these intersections contribute to unique experiences of oppression and privilege.
Can you have an intersection without a union?
Yes, you can find the intersection of sets without considering their union.
What is the importance of unions and intersections in databases?
They are used in database queries to combine or compare different datasets based on specified criteria.
In the context of labor, what is a union?
A labor union is an organization of workers formed to protect their rights and interests.
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Written by
Tayyaba RehmanTayyaba Rehman is a distinguished writer, currently serving as a primary contributor to askdifference.com. As a researcher in semantics and etymology, Tayyaba's passion for the complexity of languages and their distinctions has found a perfect home on the platform. Tayyaba delves into the intricacies of language, distinguishing between commonly confused words and phrases, thereby providing clarity for readers worldwide.
