2025-12-02 10:57:??

Let A and B be set-theory sharing some but not all elements.

A \cap B \neq \varnothing: "The intersection of A and B is nonempty" (They share at least one element).
A \not\subseteq B: "A is not a subset of $B$" (A has at least one element not in B). Equivalent to A \setminus B \neq \varnothing.
B \not\subseteq A: "B is not a subset of $A$" (B has at least one element not in A). Equivalent to B \setminus A \neq \varnothing.