The Dean of Students office wants to know how the seven general education courses

Chapter 5, Problem 26

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QUESTION:

The Dean of Students’ office wants to know how the seven general education courses selected by incoming freshmen are clustered. For each pair of general education courses, if 30 or more incoming freshmen register for both courses, the courses are defined as being “significantly linked.” Table 4 shows all the significant links between general education courses (indicated by a 1). Draw a graph that models the significant links between the general education courses. (Use the first letter of each course to label the vertices of the graph.)

\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline & \text { Math } & \text {Chemistry}& \text {Biology} & \text {English}&\text {Physics} &\text {History} &\text {Art} \\ \hline \text { Math } & & 1 & 1 & 1 & 1 & & \\ \hline \text { Chemistry } & 1 & & 1 & & & & \\ \hline \text { Biology } & 1 & 1 & & 1 & & 1 & \\ \hline \text { English } & 1 & & 1 & & 1 & 1 & 1 \\ \hline \text { Physics } & 1 & & & 1 & & 1 & 1 \\ \hline \text { History } & & & 1 & 1 & 1 & & 1 \\ \hline \text { Art } & & & & 1 & 1 & 1 & \\ \hline \end{array}\)

TABLE 4

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QUESTION:

The Dean of Students’ office wants to know how the seven general education courses selected by incoming freshmen are clustered. For each pair of general education courses, if 30 or more incoming freshmen register for both courses, the courses are defined as being “significantly linked.” Table 4 shows all the significant links between general education courses (indicated by a 1). Draw a graph that models the significant links between the general education courses. (Use the first letter of each course to label the vertices of the graph.)

\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline & \text { Math } & \text {Chemistry}& \text {Biology} & \text {English}&\text {Physics} &\text {History} &\text {Art} \\ \hline \text { Math } & & 1 & 1 & 1 & 1 & & \\ \hline \text { Chemistry } & 1 & & 1 & & & & \\ \hline \text { Biology } & 1 & 1 & & 1 & & 1 & \\ \hline \text { English } & 1 & & 1 & & 1 & 1 & 1 \\ \hline \text { Physics } & 1 & & & 1 & & 1 & 1 \\ \hline \text { History } & & & 1 & 1 & 1 & & 1 \\ \hline \text { Art } & & & & 1 & 1 & 1 & \\ \hline \end{array}\)

TABLE 4

ANSWER:

Step 1 of 10

Given:- The table:

\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline & \text { Math } & \text {Chemistry}& \text {Biology} & \text {English}&\text {Physics} &\text {History} &\text {Art} \\ \hline \text { Math } & & 1 & 1 & 1 & 1 & & \\ \hline \text { Chemistry } & 1 & & 1 & & & & \\ \hline \text { Biology } & 1 & 1 & & 1 & & 1 & \\ \hline \text { English } & 1 & & 1 & & 1 & 1 & 1 \\ \hline \text { Physics } & 1 & & & 1 & & 1 & 1 \\ \hline \text { History } & & & 1 & 1 & 1 & & 1 \\ \hline \text { Art } & & & & 1 & 1 & 1 & \\ \hline \end{array}\)

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