# Bound on volume of Minkowski Difference

$$A-B:=\{c:B+c\subseteq A\}.$$

I think that if $$A-B$$ is not the universe, then $$vol(A-B)\leq vol(A)$$ (If $$B$$ has one point then the inequality is immediate, adding more points to $$B$$ further reduces $$vol(A-B)$$ by set theoretic consideration.) Is there anything tighter?