Which of the following are TRUE for Treponema pallidum?
P. It is the causative agent of syphilis
Q. It is a spirochete
R. It is a non-motile bacterium
S. It is generally susceptible to penicillin
Choose the correct combination.
(A) P, Q and R only (B) P, Q and S only (C) P, R and S only (D) Q, R and S only
Options:
(A) P, Q and R only
(B) P, Q and S only
(C) P, R and S only
(D) Q, R and S only
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2016 Q.04)**
**1. Governing Concept & Question Classification**:
- **Section**: General Aptitude (GA)
- **Question Type**: **MCQ** (1 Mark)
- **Topic**: Propositional Logic (Conditional Statements & Implication)
**2. Detailed Step-by-Step Derivation**:
- Given the premise (Fact):
$\text{“If it rains } (P)\text{, then the field is wet } (Q)\text{”} \quad (P \implies Q)$
- In classical logic:
- Statement (i): It rains ($P$).
- Statement (ii): The field is not wet ($\neg Q$).
- Statement (iii): The field is wet ($Q$).
- Statement (iv): It did not rain ($\neg P$).
- Let us evaluate each option to find which is **NOT logically possible**:
- **Option (B)**: *“If (i), then (iii)”* $\equiv P \implies Q$. This is the given fact itself (Modus Ponens); completely valid.
- **Option (D)**: *“If (ii), then (iv)”* $\equiv \neg Q \implies \neg P$. This is the contrapositive of $P \implies Q$, which is logically equivalent to the fact; completely valid.
- **Option (A)**: *“If (iii), then (iv)”* $\equiv Q \implies \neg P$. If the field is wet, it could be wet because of a sprinkler; it is logically possible that it did not rain.
- **Option (C)**: *“If (i), then (ii)”* $\equiv P \implies \neg Q$. If it rains, the field cannot be *not wet* because the premise guarantees that whenever it rains, the field IS wet ($P \implies Q$). Therefore, $P \implies \neg Q$ is a direct contradiction of the established fact and is **NOT logically possible**.
- **Option-by-Option Evaluation**:
- **Option (A) [INCORRECT]**: Logically possible (field could be wet from other sources).
- **Option (B) [INCORRECT]**: Logically true (direct statement of fact).
- **Option (C) [CORRECT]**: Direct contradiction of the fact ($P \implies Q$), hence logically impossible.
- **Option (D) [INCORRECT]**: Logically true (contrapositive of the fact).
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **C**
- **Scoring Criteria**: +1.0 Mark (Negative marking: -0.33 marks).
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