GATE CS 2021 Set 1 — Question 9

Let $B$ be the set of bacteria, $P$ be the set of pathogens, and $M$ be the set of microorganisms.From Statement 1: All bacteria are microorganisms $\implies B \subseteq M$.
From Statement 2: All pathogens are microorganisms $\implies P \subseteq M$.We are analyzing the relationship between $P$ and $B$. Since both are subsets of $M$, they might be disjoint ($P \cap B = \emptyset$), they might overlap ($P \cap B \neq \emptyset$), or one might be a subset of the other. The premises do not force any specific relationship between $P$ and $B$.Conclusion I: "Some pathogens are bacteria" implies $P \cap B \neq \emptyset$. This does not necessarily follow.
Conclusion II: "All pathogens are not bacteria" is standardly interpreted in syllogisms as "No pathogens are bacteria" ($P \cap B = \emptyset$). This does not necessarily follow.However, the two conclusions are contradictories (assuming $P$ is not empty): either $P$ and $B$ have a non-empty intersection (Conclusion I) or they have an empty intersection (Conclusion II). One of these must be true. Therefore, logically, Either conclusion I or II is correct.Note: The official GATE 2021 answer key accepts both (C) and (D). Option (D) is valid if one interprets the question as asking which conclusion deductively follows from the premises (neither does). Option (C) is valid if one considers the logical truth that one of the two complementary possibilities must hold.