GATE CS 2021 Set 1 Q9 — General Aptitude

To analyze the given statements, let us represent them using set theory:

• Statement 1: All bacteria ($B$) are microorganisms ($M$) ⇒ $B \subseteq M$
• Statement 2: All pathogens ($P$) are microorganisms ($M$) ⇒ $P \subseteq M$

From these statements, we know that both sets $B$ and $P$ lie inside the larger set $M$. However, the relationship between $B$ and $P$ is completely undetermined. They could be disjoint, partially overlapping, or one could be a subset of the other.

Case 1: Justification for Option C (Either conclusion I or II is correct)

In classical syllogism, the statement "All pathogens are not bacteria" is interpreted as "No pathogens are bacteria" ($P \cap B = \emptyset$).

• Conclusion I: Some pathogens are bacteria ($P \cap B \neq \emptyset$).
• Conclusion II: No pathogens are bacteria ($P \cap B = \emptyset$).

Since these two scenarios ($P \cap B \neq \emptyset$ and $P \cap B = \emptyset$) are mutually exclusive and exhaustive, one of them must always be true. Therefore, either conclusion I or II is correct.

Case 2: Justification for Option D (Neither conclusion I nor II is correct)

In standard deductive logic, a conclusion is considered "correct" only if it must logically follow from the premises in all possible scenarios.

• Conclusion I ($P \cap B \neq \emptyset$) is not guaranteed, because $P$ and $B$ can be disjoint.
• Conclusion II (whether interpreted as "No $P$ is $B$" or "Not all $P$ are $B$") is also not guaranteed, because $P$ could be a subset of $B$ ($P \subseteq B$).

Since neither conclusion can be definitively deduced from the given premises, neither conclusion I nor II is correct.

Due to these two valid logical interpretations, both C and D are correct options.