Union and Intersection

Before we go into the differences between the two set operators union and intersection, let’s first go through the notion of set theory. Set theory is a fundamental subject of mathematics that investigates sets, specifically whether an item belongs to or does not belong to a set of things that are mathematically meaningful. A set is essentially a collection of well-defined things, such as integers or functions, that may or may not be mathematically relevant. A set’s items are known as elements, and they might be anything from numbers to people to vehicles to states. Almost anything and any number of components may be combined to form a set.

Union and Intersection

The union of two sets A and B is defined as the set of elements that belong to either A or B, or perhaps both. It is simply defined as the collection of all unique components or members belonging to any of these sets. The symbol represents the union operator, which is equivalent to the logical OR. It’s the smallest collection that includes everything from both sets. If set A ={ 1, 2, 3, 4, 5}, and set B ={ 3, 4, 6, 7, 9}, the union of the two sets is AB, which is written as 1, 2, 3, 4, 5, 6, 7, 9. Because the numbers 3 and 4 occur in both sets A and B, there is no need to repeat them. The number of items in the union of A and B is plainly fewer than the sum of the distinct sets since only a few numbers are shared by both sets.

The intersection of two sets A and B is defined as the set of elements that belong to both. It’s simply defined as the set that includes all members of set A who are also members of set B, as well as all elements of set B who are also members of set A. The sign represents the intersection operator, which corresponds to the logical AND. On the other hand, the intersection of two sets is the largest set, including all of the objects shared by both sets. For example, if set A={ 1, 2, 3, 4, 5}, and set B={ 3, 4, 6, 7, 9}, the intersection of the two sets is AB, which is written as 3, 4. The numbers 3 and 4 are referred to as the sets’ intersection since they are shared by both sets A and B.

Properties of union and intersection

The qualities of set intersection are comparable to the properties of numbers. The commutative law, associative law, law of null set and universal set, and idempotent law are all characteristics of set intersection.

(A B) is the set of all items shared by both sets A and B.

If A B =, then A and B are said to be distinct sets.

n(A B) = n(A) + n(B) + n(A B) – n(A B)

When executing a union of sets, it is critical to consider these features.

The union of any two sets yields a totally new set including the items from both original sets.

The resulting set comprises all items that are present in either the first or second set, or elements that are present in both sets.

The union of two disjoint sets yields a set that contains entries from both sets.

The order of the operating sets has no effect on the resulting set because of the union’s commutative feature.

Use the formula: n(A B) = n(A) + n(B) – n(A B) to get the cardinal number of the union of sets.

Differences of union and intersection

A union of two sets is a set that contains all of the values from both sets after eliminating the duplicate values. The term ‘intersection’ in mathematics refers to the shared members of different sets.

The symbol for a union is U, and the symbol for an intersection is.

A union removes redundant values. An intersection is a set with solely shared values.

The number of elements in a union is higher than or equal to the number of elements in parent sets. The number of elements in an intersection is always fewer than or equal to the number of elements in the parent sets.

A union is the addition of sets in practice. However, intersection is not the same as set subtraction.

Conclusion

The terms ‘union’ and ‘intersection’ are used differently in this context. Union means to add, and intersect means to meet. The union may be obtained by simply adding the two sets. A set with shared values is formed by the intersection of two sets.

Union and intersection are essential mathematical concepts. They are employed in the solution of sets. A solid knowledge of union and intersection allows you to readily handle tough problems.