When testing a program, testers need to generate a set of test cases that satisfies a testing objective. This set of test cases is referred to as a test suite. Usually, the generated test suite may contain redundancy, that is, some test cases may be removed from the test suite without rendering the satisfaction of the testing objective. A representative set is a subset of a test suite that satisfies the same testing objective, and test suite reduction is aimed at finding the representative sets. This paper studies the properties of representative sets related to the divide-and-conquer approach towards test suite reduction. The results provide us a better understanding of the structural properties of representative sets and how to apply the divide-and-conquer approach towards test suite reduction.