Sets are a fundamental concept in mathematics and computer science. They are collections of distinct elements, where the order of the elements does not matter. Each element within a set is unique and appears only once.

Sets are often denoted by curly braces ({}) and list their elements within the braces, separated by commas. For example, a set containing the numbers 1, 2, and 3 would be written as {1, 2, 3}. If an element appears more than once, it is still considered as a single element within the set.

Here are a few important terms related to sets:

1. Elements: The individual objects or values that make up a set. For example, in the set {1, 2, 3}, the numbers 1, 2, and 3 are the elements.
2. Cardinality: The cardinality of a set refers to the number of elements it contains. For example, the set {1, 2, 3} has a cardinality of 3.
3. Subset: A set A is said to be a subset of another set B if all the elements of A are also present in B. The symbol ⊆ is used to denote the subset relationship. For example, if A = {1, 2} and B = {1, 2, 3}, then A is a subset of B, denoted as A ⊆ B.
4. Superset: A set A is considered a superset of another set B if all the elements of B are also present in A. The symbol ⊇ is used to denote the superset relationship. For example, using the sets from the previous example, B is a superset of A, denoted as B ⊇ A.
5. Union: The union of two sets A and B is the set that contains all the elements present in either A or B, without repetition. The symbol ∪ is used to represent the union operation. For example, if A = {1, 2} and B = {2, 3}, then A ∪ B = {1, 2, 3}.
6. Intersection: The intersection of two sets A and B is the set that contains all the elements present in both A and B. The symbol ∩ is used to represent the intersection operation. For example, using the sets from the previous example, A ∩ B = {2}.
7. Empty Set: The empty set, denoted by ∅ or {}, is a set that contains no elements.

Sets provide a foundation for various mathematical operations and concepts, such as set theory, combinatorics, and probability theory. They are also widely used in computer science and programming languages to handle collections of data without duplication.