Sets, Relations and Functions
Number of Subsets (Power Set Cardinality)
Gives the total number of subsets of a finite set with n elements.
Distributive Laws of Sets
Distributes set intersection over union and set union over intersection.
De Morgan's Laws for Sets
Relates the complement of unions and intersections to the intersection and union of complements.
Set Difference Identity
Expresses the difference of two sets as the intersection with the complement.
Symmetric Difference of Sets
Gives the set of all elements belonging to either of the two sets but not both.
Inclusion-Exclusion Principle (Two Sets)
Gives the number of elements in the union of two finite sets.
Inclusion-Exclusion Principle (Three Sets)
Gives the number of elements in the union of three finite sets.
Cardinality of Cartesian Product
Gives the number of elements in the Cartesian product of two finite sets.
Total Number of Relations Between Two Sets
Gives the total number of binary relations possible from set A to set B.
Number of Reflexive Relations
Gives the total number of reflexive relations on a set of n elements.
Number of Symmetric Relations
Gives the total number of symmetric relations on a set of n elements.
Composition of Functions
Defines the composite function evaluating function f followed by function g.
Number of One-to-One Functions (Injections)
Gives the number of one-to-one functions from a set of m elements to a set of n elements.
Number of Onto Functions (Surjections)
Gives the number of onto functions from a set of m elements to a set of n elements.