Difference Between Union and Intersection

The word ‘union’ is defined as ‘an act of joining entities’ or ‘the state of being united’. The word ‘union’ has been derived from the Late Latin word ‘unus’ and the Latin word ‘unio’.

‘Intersection’ is ‘common entity different entities’ or ‘the act or process of crossing’. The word ‘intersection’ has been derived from the Latin word ‘intersectionem’.

Key Takeaways

1. Union is a set operation that combines all the elements of two or more sets without duplication, creating a new set that contains every unique element from the original sets.
2. The intersection is a set operation that identifies the common elements shared by two or more sets, creating a new set containing only those shared elements.
3. Both union and intersection are fundamental operations in set theory, but they serve different purposes: union unifies sets, while intersection identifies shared elements.

Union vs Intersection

The difference between union and intersection can be compared based on their general definitions, mathematical definitions, symbolic representations, logical inferences, process characteristics and examples.

Let us understand how to use the word ‘union’ in a sentence. For example, ‘The union of technology from the United States of America and the workforce from India can manufacture millions of vaccine doses daily’.

Now let us understand how to use the word ‘intersection’ in a sentence. For example, ‘the accident occurred at the intersection of the Prince Louis Road and Queen Elizabeth Road’.

 

Comparison Table

Parameter of Comparison	Union	Intersection
General Definition	It is defined as the act of adding or joining different entities	It is defined as the act of crossing different entities
Mathematical Definition	The union of multiple sets is defined as the set which holds all the values from all the considered sets.	The intersection of multiple sets is defined as the set which holds the common values from all the considered sets.
Symbolic Representation	U represent it.	It is represented by ∩.
Logical Inference	It is equivalent to ‘or’.	It is equivalent to ‘and’.
Process Characteristics	Union of multiple sets discards duplicate values.	The union of multiple sets only accepts the common values from
Examples	The union of opposition keeps the ruling party on their toes.	It is an intersection point of the two series.

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What is Union?

The word ‘union’ can be used rightfully when we want to add specific quantities or entities. The word ‘union’ is technically associated with politics, mathematics and economics.

Politically, the word ‘union’ means ‘joining of political parties’. Parties unite two form a stronger alliance.

The two major types of unions are:

1. Union of States
2. Union of Political Parties

The Union of states results in the formation of a stronger nation. For example, the United States of America is a union of fifty states. 

The number of elements in the union of multiple sets is always bigger than the number of elements in the parent sets. 

This can be explained with the following example:

Let us consider the two sets, A and B

1. A={violet, grey, black, brown, indigo, blue, green, yellow, orange, red} 
2. B={white, yellow, grey, black, red, violet, brown, silver, purple, blue }

The Union of the two sets A and B can be written as A U B. Let the union of the two sets be Z.

A U B= {violet, indigo, blue, green, yellow, orange, red, white, grey, black, brown, silver, purple,}

Set A consists of ten elements, and set B consists of nine. The union set Z consists of thirteen elements.

 

What is Intersection?

The word ‘intersection’ is used when discussing the point of commonality among different entities. It is the point of crossing two entities.

The intersection of multiple sets is a set which contains the shared values that are present in all the sets. Intersection only considers the expected value.

Let us consider a set X consisting of alphabets and a set Y consisting of vowels.

X={a,b,e,h,z,m,o,s}

Y={a,e,i,o,u}

The intersection of the two sets can be written as X ∩ Y. 

X ∩ Y={a,e,o}

Only three elements are common in both sets. 

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Main Differences Between Union and Intersection

1. Mathematically, a union of two sets consists of all the values from both sets removing the duplicate values. Mathematically, the word ‘intersection’ means the familiar elements from multiple sets.
2. U represent a union, and an intersection is represented by  ∩.
3. A union discards duplicated values. An intersection is a set of shared values only.
4. The number of elements of a union is greater than or equal to parent sets. The number of elements in an intersection is always less than or equal to parent sets.
5. In practice, a union is the addition of sets. But intersection is not the subtraction of sets.

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References

1. https://hal.inria.fr/docs/00/07/44/12/PDF/RR-2259.pdf
2. https://www.worldscientific.com/doi/abs/10.1142/S0129054108005838