The following table shows the results of a survey of authors by a fictitious publishing company. $$\begin{array} { | l | l | l | l | }
\hline & \text { New Authors } & \begin{array} { l }
\text { Established } \
\text { Authors }
\end{array} & \text { Total } \
\hline \text { Successful } & 2 & 25 & 27 \
\hline \text { Unsuccessful } & 14 & 56 & 70 \
\hline \text { Total } & 16 & 81 & 97 \
\hline
\end{array}$$ Consider the following subsets of the set S of all authors represented in the table: C, the set of successful authors; U, the set of unsuccessful authors; N, the set of new authors; and E, the set of established authors. Find the number of elements that set contains.
Use the table to compute $n ( C \cup N )$ .

A)43
B) 25
C) 45
D) 14
E) 41

Question

The following table shows the results of a survey of authors by a fictitious publishing company. $$\begin{array} { | l | l | l | l | } 
\hline & \text { New Authors } & \begin{array} { l } 
\text { Established } \
\text { Authors }
\end{array} & \text { Total } \
\hline \text { Successful } & 2 & 25 & 27 \
\hline \text { Unsuccessful } & 14 & 56 & 70 \
\hline \text { Total } & 16 & 81 & 97 \
\hline
\end{array}$$   Consider the following subsets of the set S of all authors represented in the table: C, the set of successful authors; U, the set of unsuccessful authors; N, the set of new authors; and E, the set of established authors. Find the number of elements that set contains.
Use the table to compute $n ( C \cup N )$ .
 
A)43
B) 25
C) 45
D) 14
E) 41

Quizplus · Accepted Answer

The set $C \cup N$ includes all successful authors and all new authors. From the table, there are 27 successful authors and 16 new authors. However, among the new authors, 2 are already counted as successful. Therefore, to avoid double-counting, we add the total number of successful authors (27) to the total number of new authors (16) and subtract the successful new authors (2) who are counted in both categories: $27 + 16 - 2 = 41$.

The Following Table Shows the Results of a Survey of Authors