This paper considers various problems of recognizing the properties of decision rule systems. Deterministic and nondeterministic decision trees are used as algorithms for solving them. It is proved that the minimum depth of a deterministic decision tree solving the problem is bounded from above by the square of the minimum depth of a nondeterministic decision tree. Note that a nondeterministic decision tree can be considered as a representation of a system of decision rules that are true for the problem under consideration and cover all possible inputs. The results obtained may be of interest to the rough set theory, in which both decision rule systems and decision trees are intensively studied. In particular, they make one think about the possibilities of transforming decision rule systems into decision trees.