Background

What does it mean if 2 sets are dispoint?

A n B = empty set. The 2 sets share no common elements

What does it mean if a collection of sets are pairwise disjoint?

If any two distinct sets within that collection have an empty intersection, meaning they share no common elements

Given a set Ω and subsets A, B ⊆ Ω. How do you write the union A U B?

A U B := {w ∈ Ω: w ∈ A or w ∈ B}

Given a set Ω and subsets A, B ⊆ Ω. How do you write the intersection A n B?

A n B := {w ∈ Ω: w ∈ A and w ∈ B}

Given a set Ω and subsets A, B ⊆ Ω. How do you write the complementary set A^c?

A^c := {w ∈ Ω: w ∉ A}

Given a set Ω and subsets A, B ⊆ Ω. How do you write the set difference A\B?

A\B := {w ∈ Ω: w ∈ A and w ∉ B}

What is the formula for sum of arithmetic series?

(n + 1)n/2

What is the formula for sum of geometric series?

(1 - xⁿ⁺¹)/(1 - x)

What is the formula for the sum of an infinite series?

1/(1 - x)