Set Theory
Sets - collections of elements
x ∈ A = x is in set A
x ∉ A = x is not in set A
Ac = the set of things not in set A; the complement of A
B ⊂ A = B is a subset of A; every element of set B is in set A
If B ⊂ A but A ≠ B, B is a proper subset of A
A ∪ B - The union of A and B; the event that either A or B occurs
A ∩ B - The intersection of A and B; the event that both A and B occur
A / B - The difference between sets; the set of elements that are in A, but not B
Ac - The complement of A; the event that A does not occur
θ = The empty set; the set with no elements
(A ∪ B)c = Ac ∩ Bc
(A ∩ B)c = Ac ∪ Bc
(A ∩ Ac) = θ
If B ⊂ A, then A ∪ B = A and A ∩ B = B
(A ∪ B) ∩ C = (A ∩ C) ∪ (B ∩ C)
(A ∩ B) ∪ C = (A ∩ C) ∪ (B ∩ C)
Cartesian Product: pairs of elements, with the first element in the first set, and the second element in the second set
A x B = {(a,b), such that a ∈ A and b ∈ B}
Order matters so A x B ≠ B x A