Word for two collections that do not have any elements in common

I'm looking for a word for when you have a collection A and a collection B and they have no overlap.

In mathematical terms: the relation between two sets where the intersection is empty. Like in this Venn diagram:

The word that keeps popping up in my mind is disparate sets, but I don't feel that completely covers the meaning when I look at the definition, because that doesn't seem to preclude overlapping sets that are different:

disparate 1. distinct in kind; essentially different; dissimilar: disparate ideas.

Solution 1:

You want disjoint, as in "disjoint sets".

From Wolfram Mathworld:

Disjoint Sets

Two sets A₁ and A₂ are disjoint if their intersection A₁ ∩ A₂ = ∅, where ∅ is the empty set.

Disjoint sets are also said to be mutually exclusive or independent.

Solution 2:

You might consider orthogonal

Very different or unrelated; sharply divergent: "Radical Islamists are ultimately seeking to create something orthogonal to our model of democracy" (Richard A. Clarke). [American Heritage]

This suggest something very different, not just non-overlapping.