Functions and Relations Reference

Discrete Math · Axiom Academy

FORMULA SHEET Functions and Relations Comprehensive reference for relation properties, function classifications, and special function classes A relation R from set A to set B is a subset of the Cartesian product A × B Must be reflexive, symmetric, and transitive Must be reflexive, antisymmetric, and transitive A function is a relation where each element in A is related to exactly one element in B Read as "g composed with f" or "g of f" Domain Requirement: Range of f must be subset of domain of g Existence Theorem: A function has an inverse if and only if it is bijective Floor Function (Greatest Integer) Ceiling Function (Least Integer) where r is the remainder when a is divided by n Read as "a is congruent to b modulo n" FINDING INVERSE FUNCTIONS (ALGORITHM) Bijections (when |A| = |B| = n):

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