SETS

Set

A well-defined and unordered collection of objects called elements or members.

Element (Member)

An object that belongs to a set.

Well-Defined Set

A set where membership is clearly determined and not based on opinion.

Unordered Collection

A property of sets where the order of elements does not matter.

Capital Letter Notation

Sets are usually represented using uppercase letters (e.g., A, B, S).

Roster Method (Listing Method)

A way of writing a set by listing all its elements inside braces.

Set-Builder Method (Descriptive Method)

A way of writing a set by describing the properties of its elements.

Universal Set (U)

The set that contains all elements relevant to a particular discussion.

Element Notation (∈)

A symbol meaning “is an element of.”

Not an Element (∉)

A symbol meaning “is not an element of.”

Finite Set

A set with a countable number of elements.

Infinite Set

A set with a countable number of elements.

Ellipsis ( … )

A symbol used to show that a set continues indefinitely.

Set Equality

Two sets are equal if they contain exactly the same elements.

Duplicate Elements

Repeated elements in a set, which are ignored since duplicates do not affect sets.

Subset (⊆)

A set whose elements are all contained within another set.

Proper Subset (⊂)

A subset that is not equal to the set it is contained in.

Improper Subset

A subset that is equal to the set itself.

Number of Subsets

The total number of subsets of a set with n elements, given by 2ⁿ.

Number of Proper Subsets

The total number of proper subsets of a set with n elements, given by 2ⁿ − 1.

Venn Diagram

A visual representation of sets using circles inside a rectangle representing the universal set.

Algebra of Sets

The study of operations and relationships between sets.

Complement of a Set (A’ or Aᶜ)

The set of all elements in the universal set that are not in set A.

Intersection (∩)

The set of elements common to both sets.

Union (∪)

The set of all elements that are in either set or both sets.

Set Difference (−)

The set of elements that are in one set but not in another.

Symmetric Difference (⊕)

The set of elements that are in either of the sets but not in both.

Null Set (∅)

A set that contains no elements.

Counting Elements

Determining the number of elements in a set.

Word Problem (Set Context)

A problem that uses real-life situations and sets, often solved using Venn diagrams.