WGU C959 Unit 2 Sets and Subsets

Union; A ∪ B

{x : x ∈ A or x ∈ B}

Intersection; A ∩ B

{x : x ∈ A and x ∈ B}

Symmetric difference A ⊕ B

(A − B) ∪ (B − A); A or B but not both

Cartesian product A × B

{(a,b) : a ∈ A, b ∈ B}; First entry in A, second in B; Cardinality |A × B| = |A| · |B|

{0,1}ⁿ

Set of binary strings of length n

Power set P(A)

Set of all subsets (not elements) of A; Cardinality |P(A)| = 2^|A|

Disjoint

No elements in common; A and B are disjoint if their intersection is empty (A ∩ B = ∅ )

Partition

A partition of set S is a collection of non-empty subsets {A₁, A₂, …, Aₙ} such that every element of S is in exactly one subset (the subsets are pairwise disjoint and their union is S).

Pairwise disjoint

A sequence of 3 or more sets where every pair of sets has no element in common; Every pair of distinct sets in the sequence is disjoint

Function f(x) = y

For every input x, there is exactly one output y

A ⊆ B

A is a subset of B; every element of A is in B

A ⊂ B

A is a proper subset of B; A ⊆ B and A ≠ B