### **Detailed Step-by-Step Solution (GATE AE 2017 Q.58)**
**1. Intuitive Physical Setup & Given Parameters**:
- Rule conditional statement: $\text{Drinking Beer} \implies \text{Age} > 18$ ($P \implies Q$).
- Contrapositive: $\text{Age} \le 18 \implies \text{NOT Drinking Beer}$ ($\neg Q \implies \neg P$).
- Observed individuals:
- Person P: Drinking beer (condition $P$)
- Person Q: Drinking coke (condition $\neg P$)
- Person R: 16 years old (condition $\neg Q$)
- Person S: 25 years old (condition $Q$)
**2. Step-by-Step Logical Derivation**:
1. **Modus Ponens (Checking P)**:
Person P is drinking beer. We must verify that Person P is
gt; 18$. If they are $\le 18$, the rule is violated. Therefore, **Person P must be checked**.
2. **Checking Person Q (Drinking coke)**:
The rule specifies nothing about people drinking non-alcoholic beverages. Anyone can drink coke regardless of age. No violation possible. Do NOT check Q.
3. **Modus Tollens (Checking R)**:
Person R is 16 years old ($\le 18$). If Person R is drinking beer, the rule is violated. Therefore, **Person R must be checked**.
4. **Checking Person S (25 years old)**:
Person S is
gt; 18$. A person over 18 is permitted to drink beer or coke. No violation possible. Do NOT check S.
5. Consequently, exactly **P and R** must be inspected.
**3. Comprehensive Options & Distractor Analysis**:
- **(A)** P only: ❌ Incorrect. Omits checking the underage person R.
- **(B)** P and R only: ✅ **CORRECT**. Classical solution to the Wason Selection Task ($P$ and $\neg Q$).
- **(C)** P and S only: ❌ Incorrect.
- **(D)** Q and R only: ❌ Incorrect.
**4. Official Master Key & Exam Takeaway**:
- **Official Answer**: **B**
- **Logical Principle**: To test $P \implies Q$, you must always inspect $P$ (to see if $Q$ holds) and $\neg Q$ (to see if $\neg P$ holds).