Discrete Mathematics - Sets

These flashcards cover key vocabulary and concepts from the lecture on Discrete Mathematics, focusing on sets.

Discrete Mathematics

The study of mathematical objects that can assume only countable or distinct values.

Set

A collection of distinct objects, often referred to as elements or members.

Cardinality

The number of elements in a set, denoted as |X| for a finite set X.

Proper Subset

A set X is a proper subset of set Y if all elements of X are in Y and X is not equal to Y.

Set-builder Notation

A notation for describing a set by a property that its members must satisfy.

Union of Sets (X ∪ Y)

A set containing all elements that are in either set X or set Y.

Intersection of Sets (X ∩ Y)

A set containing all elements that are in both set X and set Y.

Empty Set

The set with no elements, denoted as {} or ∅.

Venn Diagram

A diagram that pictorially represents sets and their relationships.

Cartesian Product (X × Y)

The set of all ordered pairs (a, b) where a is an element of set X and b is an element of set Y.