Are you confused about the differences between union and intersection? Do these terms sound like gibberish to you?
Union refers to the combination of two sets, resulting in a new set that contains all unique elements from both sets. While intersection refers to the common elements shared by two sets, creating a new set with only those elements.
Union vs. Intersection
| Union | Intersection |
|---|---|
| The union of two sets combines all the elements from both sets, creating a new set that includes every unique element present in either set. It captures the idea of combining or merging sets. | The intersection of two sets identifies and selects the elements that are common to both sets, resulting in a new set that contains only those shared elements. It captures the concept of finding the overlap between sets. |
| Its operation results in a new set that contains all the distinct elements from both input sets, eliminating any duplicates. It ensures that each element appears only once in the union set. | Its operation yields a new set that consists of the elements that exist in both input sets. It captures the elements that are present in the overlap or intersection of the two sets. |
| Union set can be larger than the individual input sets if there are elements that are unique to each set. The union set will contain all the unique elements from both sets, including any duplicates found within each set. | Intersection set can be smaller than the individual input sets since it includes only the elements that are common to both sets. It excludes any elements that exist exclusively in either set. |
| It is an inclusive operation that combines all elements from both sets into the resulting set. It does not exclude any elements, including duplicates that might exist within each set. | It is an exclusive operation that selects only the elements that are shared by both sets. It excludes any elements that are unique to either set, focusing solely on the common elements. |
| The union of A = {1, 2, 3} and B = {3, 4, 5} is {1, 2, 3, 4, 5}, as it combines all the unique elements from both sets, resulting in a set that includes every distinct element. | The intersection of A = {1, 2, 3} and B = {3, 4, 5} is {3}, representing the only element that is common to both sets. It captures the overlap or shared element between the two sets. |
What is the Union?
The union is a set operation that combines two or more sets to create a new set that contains all the unique elements from the input sets. It is the process of merging sets to form a larger set that includes all distinct elements without any duplicates. The union operation is denoted by the symbol “∪”.
What is the Intersection?
The intersection is a set operation that identifies and selects the common elements shared by two or more sets. It creates a new set that contains only those elements that exist in all of the input sets.
The intersection captures the overlap or the elements that are present in every set being considered. The intersection operation is denoted by the symbol “∩”.
Common uses of union and intersection
One, when you’re trying to find all the items that belong to both sets. For instance, let’s say you have a set of numbers that represent the ages of all the members of your family, and another set of numbers that represent the ages of all the members of your spouse’s family. If you want to find out how many people there are in total between both families, you would take the union of these two sets.
Another common scenario is when you’re trying to figure out what items are different between two sets. For example, let’s say you have a set of numbers that represent the temperatures on various days last week, and another set of numbers that represent the temperatures on various days this week. If you want to know which days last week were warmer than this week, you would take the intersection of these two sets.
Examples of union and intersection
Union
The union of two sets is the set of all elements that belong to either set. If we have two sets A and B, the union of A and B would be denoted as A ∪ B. The union of A and B would include all elements that are in A, all elements that are in B, and all elements that are in both A and B.
Set A = {1, 2, 3}
Set B = {3, 4, 5}
The union of A and B would be denoted as A ∪ B = {1, 2, 3, 4, 5}. So, as you can see from this example, the union of two sets includes all elements from both sets.
Intersection
The intersection of two sets is the set of all elements that belong to both sets. If we have two sets A and B again, the intersection of A and B would be denoted as A ∩ B. The intersection of A and B would only include those elements that are in both A and B.
Set A = {1, 2, 3}
Set B = {3, 4, 5}
The intersection of A and B would be denoted as A ∩ B = {3}.
Key differences between the union and intersection
- Purpose:
- Union: The purpose of the union is to combine sets and create a new set that includes all unique elements from the input sets.
- Intersection: The purpose of the intersection is to select and create a new set that contains only the elements common to all input sets.
- Result:
- Union: The result of the union operation is a new set that contains all the unique elements from the input sets.
- Intersection: The result of the intersection operation is a new set that includes only the elements shared by all input sets.
- Size:
- Union: The size of the union set can be larger than the individual input sets since it includes all unique elements.
- Intersection: The size of the intersection set can be smaller than the input sets as it consists of only the shared elements.
- Operation:
- Union: Union is an inclusive operation that combines elements from both sets without excluding any.
- Intersection: Intersection is an exclusive operation that selects only the common elements and excludes the non-shared ones.
- Difference between Odds and Probability
- Difference between Sequence and Series
- Difference between Definite and Indefinite Integrals
Conclusion
The union combines sets, creating a new set that includes all unique elements from the input sets. While the intersection identifies and selects the common elements shared by the input sets, creating a new set with only those elements. These differences highlight the contrasting nature of the union and intersection operations in set theory.
