Discrete Mathematics – MATH 1006: Lecture 4

These flashcards cover key vocabulary and concepts from Lecture 4 of the Discrete Mathematics course.

Counting Problem

A problem that requires determining the number of ways to select or arrange items according to specific rules.

Inclusion-Exclusion Principle

A formula to calculate the size of the union of two sets: |A ∪ B| = |A| + |B| − |A ∩ B|.

Cartesian Product

The set of all ordered pairs (a, b) where a is from set A and b is from set B, denoted as A × B.

Injective Function

A function where each element of the codomain is mapped by at most one element of the domain.

Surjective Function

A function where every element in the codomain is mapped by at least one element of the domain.

Bijection

A function that is both injective and surjective, establishing a one-to-one correspondence between two sets.

Permutation

An arrangement of all the members of a set into a sequence or order.

Multiplication Principle

The total number of combinations of two tasks is the product of the number of ways to perform each task.

Ordered Selections

Selections where the order in which items are selected is significant.

Disjoint Sets

Two sets that have no elements in common, i.e., their intersection is empty.