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This paper undergoes quantitative analyses on fundamental properties of ad hoc networks including estimating the number of hiddenterminal pairs and the number of exposed-terminal sets. To obtain these results, we propose a paradigm to systematically derive exact formulas for a great deal of subgraph probabilities of random geometric graphs. In contrast to previous work, which established asymptotic bounds or approximation, we obtain closed-form formulas that are fairly accurate and of practical value.