  In this paper, we prove an inequality on the cardinalities of the minimum
size global defensive alliance and the minimum size global offensive alliance.
A global defensive alliance is a dominating set such that when any point inside
a selected group $S$ is chosen, at least half of the points in its neighborhood
are also in the set $S$, including the selected point. A global offensive
alliance is a dominating set such that if any point outside $S$ is selected, at
least half of the points in its neighborhood, including the selected point, are
in set $S$. Our result answers an open question in [HA].
