In mathematics, a set is a collection of different things, called elements or members of the set. A set may also be called a collection or family, especially when its elements are themselves sets; this may avoid confusion between the set and its members.
Sets are defined as a collection of distinct elements. The elements of a set share a common characteristic among them. Learn about sets definition, representation, types, symbols, formulas, and their properties with some solved examples.
If A and B are two sets and at least one element from A is present in B or vice versa, then the two sets A and B are said to be overlapping. For example, if A = {1, 2, 3, 4} and B = {3, 4, 5, 6, 7}, then elements 3 and 4 are common in both sets A and B.
Sets in math are also defined in the similar context. In mathematics, a set is defined as a collection of distinct, well-defined objects forming a group. There can be any number of items, be it a collection of whole numbers, months of a year, types of birds, and so on. Each item in the set is known as an element of the set.
This section introduces the basics of Set Theory, helping you understand key concepts like types of sets, set operations, and important formulas through clear examples and symbols.
Definition Empty set, denoted by φ, is a set with no elements. Definition Two sets are called disjoint if, and only if, they have no elements in common. Problems Let A = {1, 3, 5} and B = {2, 4, 6}. Are A and B disjoint?