## Thinking Mathematically (6th Edition)

RECALL: Set $A$ is a proper subset of set $B$ if all elements of $A$ are also elements of $B$ but $A\ne B$. In other words, all elements of A are also elements of B, but $B$ has at least one element that is not in A. The empty set is a proper subset of any non-empty set is the non-empty set has at least one element that is not in the empty set. However, the empty set is not a proper set of itself. Thus, the statement is false.