1. **State the problem:** We are given three hypotheses: - Randy works hard (denote as $P$). - If Randy works hard, then he is a dull boy (denote as $P \to Q$). - If Randy is a dull boy, then he will not get the job (denote as $Q \to R$). We want to show that these imply the conclusion: Randy will not get the job (denote as $R$). 2. **Recall the rules of inference:** - **Modus Ponens:** From $P$ and $P \to Q$, infer $Q$. - **Hypothetical Syllogism:** From $P \to Q$ and $Q \to R$, infer $P \to R$. 3. **Apply Modus Ponens to the first two hypotheses:** Given $P$ (Randy works hard) and $P \to Q$ (If Randy works hard, then he is a dull boy), we infer $Q$ (Randy is a dull boy). 4. **Apply Modus Ponens again:** Given $Q$ (Randy is a dull boy) and $Q \to R$ (If Randy is a dull boy, then he will not get the job), we infer $R$ (Randy will not get the job). 5. **Conclusion:** By applying the rules of inference step-by-step, we have shown that the hypotheses imply the conclusion $R$. Thus, the conclusion "Randy will not get the job" logically follows from the given hypotheses.