Given below are two statements 1 and 2, and two conclusions I and II.
Statement 1: All bacteria are microorganisms.
Statement 2: All pathogens are microorganisms.
Conclusion I: Some pathogens are bacteria.
Conclusion II: All pathogens are not bacteria.
Based on the above statements and conclusions, which one of the following
options is logically CORRECT?
Options:
(A) Only conclusion I is correct
(B) Only conclusion II is correct
(C) Either conclusion I or II is correct
(D) Neither conclusion I nor II is correct
Official Answer Key:
C,D
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2021 Q.9)**
**1. Governing Concept**:
- **Topic**: Syllogisms & Venn Diagram Logic
- Statements:
1. *All bacteria are microorganisms* ($B \subseteq M$).
2. *All pathogens are microorganisms* ($P \subseteq M$).
- Both subsets $B$ and $P$ reside inside the universal set of microorganisms $M$. However, the relationship between $B$ and $P$ is unconstrained:
- They could overlap ($B \cap P \neq \emptyset$), meaning *Some pathogens are bacteria* (Conclusion I).
- They could be mutually disjoint ($B \cap P = \emptyset$), meaning *No pathogens are bacteria* / *All pathogens are not bacteria* (Conclusion II).
- Since either they share elements or they do not, Conclusions I and II form complementary conditions under Venn set intersection.
- **Official GATE Status**: Both **C** (*Either conclusion I or II is correct*) and **D** (*Neither conclusion I nor II is independently guaranteed with certainty*) were officially accepted by IIT Bombay.
**2. Option Analysis**:
- **Option (A) is INCORRECT**: Conclusion I cannot be asserted with absolute certainty.
- **Option (B) is INCORRECT**: Conclusion II cannot be asserted with absolute certainty.
- **Option (C) [Either conclusion I or II is correct] is CORRECT (Officially Accepted)**: As an either-or dichotomy of set intersection.
- **Option (D) [Neither conclusion I nor II is correct] is CORRECT (Officially Accepted)**: Neither conclusion follows with logical certainty.
**3. Final Answer**:
- **Correct Choice**: **C or D**
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