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Boolean expressions can be used in programs and specifications to describe the complex logic decisions in mission-critical, safety-critical and Web services applications. We define a topological model (T-model) to represent Boolean expressions and characterize the test data. This paper provides proofs of relevant T-model properties, employs the combinatorial design approach, and proposes a family of strategies and techniques to detect a variety of faults associated with Boolean expressions. We compare our strategies with MC/DC, MUMCUT, MANY-A, MANY-B, MAX-A and MAX-B, and conclude that T-model based approach detects more types of faults than MC/DC, MUMCUT MANY-A and MAX-A, and detects the same types but more instances of faults than MANY-B and MAX-B with much smaller test data set.