Flash Cards: Sets

A set is a well-defined collection of distinct objects, considered as an object in its own right.

Sets are usually denoted by capital letters (A, B, C) and their elements by small letters (a, b, c).

Roster form lists all elements of a set within curly braces, e.g., A = {1, 2, 3}.

Set-builder form describes elements based on a property, e.g., A = {x | x is a natural number}.

An empty set, denoted by φ or {}, contains no elements.

A finite set has a countable number of elements.

An infinite set has an uncountable number of elements.

Two sets A and B are equal if they have exactly the same elements (A = B).

A set A is a subset of B (A ⊂ B) if every element of A is also an element of B.

A proper subset A of B (A ⊂ B) contains some but not all elements of B.

The union A ∪ B is the set of elements in either A or B or both.

The intersection A ∩ B is the set of elements common to both A and B.

The difference A - B consists of elements in A that are not in B.

A Venn diagram visually represents the relationships between sets with circles and rectangles.

The universal set is the set that contains all objects under consideration, usually denoted by U.

Sets are disjoint if they have no elements in common, i.e., A ∩ B = φ.

The complement A' of set A contains all elements not in A but in the universal set U.

Assuming sets can have repeated elements; each element in a set is distinct.

A = {1, 3, 5, 7, 9} is a set of odd natural numbers less than 10.