Example 1.3 If Aaron is late, then Bill is late, and, if both Aaron and Bill are late, then class is boring. Suppose that class is not boring. What can you conclude about Aaron? Solution: Let's begin by translating the first sentence into the symbols of logic, using the following statements. p = "Aaron is late." q-"Bill is late." r-"Class is boring." 35 Let S be the statement "If Aaron is late, then Bill is late, and, if both Aaron and Bill are late, then class is boring." In symbols, S translates to the following. Now let's construct a truth table for S. We do this by constructing truth tables for the different parts of S, starting inside the parentheses and working our way out