(d Non-Trees The graphs in (a), (b), and (c) all have circuits, and the graph in
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(d Non-Trees The graphs in (a), (b), and (c) all have circuits, and the graph in (d) is not connected. Examples of Trees The following examples illustrate just a few of the many and varied situations in which mathematical trees arise. 10.5.2 ADecision Tree During orientation week, a college administers an exam to all entering students to deter- mine placement in the mathematics curriculum. The exam consists of two parts, and placement recommendations are made as indicated by the tree shown in Figure 10.5.3. Read the tree from left to right to decide what course should be recommended for a stu- dent who scored 9 on part I and 7 on part II. -10 Math 120 Score on part II s10 Math 110 26 Math 110 Score on part I Score on part 11 -S6- #8-9, 10 Math 100 Math 100 Figure 10.5.3 Solution Since the student scored 9 on part I, the score on part II is checked. Since it is greater than 6, the student should be advised to take Math 110. ple 10.5.3 A Parse Tree In the last 30 years, Noam Chomsky and others have developed new ways to describe the syntax (or grammatical structure) of natural languages such as English. As is discussed briefly in Chapter 12, this work has proved useful in constructing compilers for high- level computer languages. In the study of grammars, trees are often used to show the derivation of grammatically correct sentences from certain basic rules. Such trees are called syntactic derivation trees or parse trees.Explanation / Answer
Since the student scored 8 in Part-I, the score on Part-II is checked. Since the score on Part-II is greater than 6, so the student is recommended to take Math 110 course
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