Lecture 1 - Set Operations in Discrete Mathematics

Set

Collection of distinct objects in any order.

Set Membership

Indicates if an element belongs to a set.

Membership Notation

Symbol € indicating set membership.

Finite Set

Set with a limited number of elements.

Infinite Set

Set with an uncountable number of elements.

Set Notation

Describes elements satisfying a property: {x|p(x)}.

Union

Combines elements from two sets, removing duplicates.

Union Notation

Symbol U representing the union of sets.

Intersection

Elements common to both sets, removing duplicates.

Intersection Notation

Symbol ∩ indicating the intersection of sets.

Difference

Elements in one set not present in another.

Difference Notation

Symbol - representing the difference of sets.

Cartesian Product

Pairs each element of one set with another.

Ordered Pair

Pair of objects where order matters.

Cartesian Product Notation

Symbol X representing the Cartesian product.

Equal Ordered Pairs

Pairs <a,b> and <c,d> are equal if a=c, b=d.

Set A Example

Set A: {1,2,3,4,5,6,7}.

Set Naming Convention

Sets are named with single uppercase letters.

Set Elements Convention

Members are represented by single lowercase letters.

Hashing in Sets

Process of organizing elements for operations.

Order of Operations

Order matters in set difference, like arithmetic.