\begin{tabular}{l} Fifty two percent of students at a local college works (for pay) in addition to being \\ students, and \( 39 \% \) of the students at the school are parents. \( 14 \% \) of students fit into \\ both categories. \\ What percentage of the student body neither work nor are parents? \\ \( \begin{array}{l}21 \% \\ 20 \%\end{array} \) \\ \hline \( 22 \% \)\end{tabular}

To find the percentage of students who neither work nor are parents, we can use the principle of inclusion-exclusion. Let: - \( A \) be the set of students who work. - \( B \) be the set of students who are parents. From the problem: - \( P(A) = 52\% \) - \( P(B) = 39\% \) - \( P(A \cap B) = 14\% \) The percentage of students who either work or are parents (or both) is given by: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Substituting the values: \[ P(A \cup B) = 52\% + 39\% - 14\% = 77\% \] Now, to find the percentage of students who neither work nor are parents, we subtract the percentage of students who either work or are parents from 100%: \[ P(\text{neither A nor B}) = 100\% - P(A \cup B) = 100\% - 77\% = 23\% \] However, the provided options did not have 23%. Therefore, it's important to recheck the math or details. Unfortunately, none of these options aligns correctly with our calculations based on the given statistical data. Therefore, based on our calculation, the percentage of the student body that neither works nor are parents should be \( 23\% \).