Table of Contents
Set Operations
Union: The union of two sets is the set of all elements that are in either set.
A ∪ B = {x : x ∈ A or x ∈ B}
Intersection: The intersection of two sets is the set of all elements that are in both sets.
A ∩ B = {x : x ∈ A and x ∈ B}
Difference: The difference of two sets is the set of all elements that are in the first set but not in the second set.
A − B = {x : x ∈ A and x ∉ B}
Union of Sets
A union of sets is a set that is the result of combining two or more sets. The union is typically represented by the symbol ∪. To find the union of two sets, you simply combine the members of the sets. For example, the union of the sets {1, 2, 3} and {4, 5, 6} is the set {1, 2, 3, 4, 5, 6}.
Intersections of Sets
Intersection of sets is the set of all elements that are common to both sets. In mathematical notation, the intersection of sets A and B is written as A ∩ B.
For example, if A = {1, 2, 3} and B = {4, 5, 6}, then the intersection of A and B is {4, 5, 6}.
The intersection of A and B is a subset of both sets A and B.
Difference of Sets
Mathematically, a set is a collection of objects that are considered to be of the same type. The objects in a set can be anything from numbers to letters to objects in the real world. Two sets are said to be different if they contain different objects.
For example, the set of all letters in the alphabet is different from the set of all numbers. The set of all even numbers is different from the set of all prime numbers. And the set of all dogs is different from the set of all cats.
There are a few ways to tell if two sets are different. The easiest way is to simply count the number of objects in each set. If the sets have different numbers of objects, then they are definitely different.
Another way to tell if two sets are different is to see if they have any objects in common. If they do not have any objects in common, then they are different. However, if they do have some objects in common, then they are not different.
One example of two sets that are not different is the set of all natural numbers and the set of all whole numbers. Both of these sets contain the number 1, the number 2, the number 3, and so on. So even though the sets are different, they do have some objects in common.
Another example of two sets that are not different is the set of all English letters and the set of all Spanish letters. Both of these sets contain the letter A, the letter B, the letter C, and so on. So even though the sets are different, they do have some objects in common.
However, the set of all English letters is different from the set of all Spanish letters. The set of all English letters contains the letter A, the letter B, the letter C, and so on. The set of all Spanish letters contains the letter A, the letter Á, the letter B, and so on. So even though the sets have some objects in common, they are still different.. different..
