Logic formulas concerning sets

A ⊆ B ∧ B ⊆ A -> A = B

Cartesian product of two sets: R = A ⨯ B = { (a,b) | ∀a ∈ A ∧ ∀b ∈ B }

∀ab. (a,b) ∈ R -> a ∈ A ∧ b ∈ B

Cartesian product of a set with itself: ℕ² = ℕ ⨯ ℕ = { (n,m) | ∀n,m ∈ ℕ }