A = B
x | x ∈ A <=> x ∈ B
A U B
x| x ∈ A v x ∈ B
A ∩ B
x| x ∈ A ^ x ∈ B
A - B
x| x ∈ A ^ x ∉ B
|A U B|
|A| + |B| - |A ∩ B|
|A - B|
|A| - |A ∩ B|
A complement
x | x ∈ U ^ x ∉ A
A ⊆ B
x | x ∈ A -> x ∈ B
A ⊂ B
x | x ∈ A -> x ∈ B ^ ∃x x ∈ B ^ x ∉ A
Injective (one to one)
∀x ∀y, x ≠ y -> f(x) ≠ f(y)
each element of the codomain is mapped to by at most one element of the domain
Surjective (onto)
codomain = range
each element of the codomain is mapped to by at least one element of the domain