1. **State the problem:** We need to represent the sentence "She is not good in math and she is not doing well in English implies she will not pass the exam" in symbolic form using the given propositions: - $p$: She is not good in math. - $q$: She is doing well in English. - $r$: She will pass the exams. 2. **Analyze the sentence:** - "She is not good in math" translates as $p$. - "She is not doing well in English" means the negation of $q$, which is $\neg q$. - "She will not pass the exam" means the negation of $r$, which is $\neg r$. 3. **Form the compound statement:** - The phrase "and" corresponds to conjunction $\wedge$. - The phrase "implies" corresponds to implication $\rightarrow$. - The entire sentence becomes: $(p \wedge \neg q) \rightarrow \neg r$. 4. **Check the options:** - (a) $(p \wedge \neg q) \rightarrow \neg r$ matches the derived symbolic form. - Other options do not match the given sentence's meaning. **Final Answer:** Option (a) $(p \wedge \neg q) \rightarrow \neg r$ is the appropriate compound statement for the sentence.