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 a Latin word ‘unio’. The two words, ‘unus’ and ‘unio’, in English, means ‘one’ and ‘to unite’, respectively.

The word ‘intersection’ is ‘common entity different entities’ or ‘the act or process of crossing’. the word ‘intersection’ has been derived from the Latin word ‘intersectionem’. the word ‘intersectionem’ was coined around the mid-sixteenth century. The root word for ‘intersection’ in the English language is ‘intersect’. ‘Intersect’ means to ‘to cross’.

**Union vs Intersection**

The difference between union and intersection can be compared on the basis of 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 workforce from India, can manufacture millions of doses of vaccine every day’. Here the word ‘union’ means to join the capabilities of both the countries to manufacture the vaccine.

Now let us understand how to use the word ‘intersection’ in a sentence. For example, ‘the accident took place at the intersection of the Prince Louis Road and Queen Elizabeth Road’. Here the word ‘intersection’ means the crossing point of the two roads. It describes the common point of the two roads.

## Comparison Table Between Union and Intersection (in Tabular Form)

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 of 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 | It is represented by U. | It is represented by ∩. |

Logical Inference | It is equivalent to ‘or’. | It is equivalent to ‘and’. |

Process Characteristics | Union of multiple set discardsduplicate values. | 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. |

## What is Union?

The word ‘union’ can be used rightfully when we want to add certain 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 forms a stronger alliance.

The two major types of unions are:

- Union of States
- Union of Political Parties

Union of states results in the formation of a stronger nation. For example, the United States of America is a union of fifty states. Union of political parties means fusion of ideologies and members. The aim of forming a union is to strengthen the

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 set A and B

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

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 elements.The union set Z consists of thirteen elements.

## What is Intersection?

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

The intersection of multiple sets is a set which contains the common values that are present in all the sets. Intersection only considers the common value. This can be explained by taking the example of the biosphere. Biosphere exists only when there is the availability of land, water and air. It means biosphere is the intersection of the lithosphere, the hydrosphere and the atmosphere.

Let us consider a set X consisting of alphabets and 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 set can be written as X ∩ Y.

X ∩ Y={a,e,o}

Only three elements are common in both the sets.

**Main Differences Between Union and Intersection**

- Mathematically, a union of two sets is a set consisting of all the values from both the sets removing the duplicate values. Mathematically, the word ‘intersection’ means the common elements from multiple sets.
- A union is represented by U and intersection is represented by ∩.
- A union discards duplicates values. An intersection is a set of common values only.
- 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.
- In practice, a union is the addition of sets. But intersection is not the subtraction of sets.

## Conclusion

The words ‘union’ and ‘intersection’ are used in a different context. Union means to add and intersect means the common points. The union can be simply found by adding the two sets. The intersection of two sets is a set having common values.

Union and intersection are an important concept in mathematics. They are used in solving sets. Good understanding of union and intersection helps to solve difficult questions easily.

## References

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

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