Given below are two statements and two conclusions:
Statement 1: All bacteria are microorganisms.
Statement 2: All pathogens are microorganisms.
Conclusion I: Some pathogens are bacteria.
Conclusion II: No clean object is a soap.
Conclusion III: Some clean objects are soaps.
Conclusion IV: All wet objects are soaps.
Based on the above statements and conclusions, which one of the following options is logically CORRECT?
A. Only conclusion I is correct
B. Either conclusion I or conclusion II is correct
C. Either conclusion III or conclusion IV is correct
D. Neither conclusion I nor conclusion II is correct
GATE 2021 · General Aptitude · Statements Follow · medium
Answer: C and D
Check Conclusion I: Some pathogens are bacteria: From 'all bacteria are microorganisms' and 'all pathogens are microorganisms', we cannot conclude their intersection is non-empty. The Venn diagram shows bacteria and pathogens can be completely separate circles inside microorganisms. Conclusion I is NOT necessarily true.
Check Conclusion II: No clean object is a soap (or equivalent negative conclusion): The premises say nothing about clean objects or soaps. Any conclusion about soaps cannot be derived from the given statements. Conclusion II is NOT derivable. Similarly, 'All pathogens are not bacteria' (another stated conclusion) is not guaranteed either.
Apply the answer key: Official answer is C and D. Option C says 'Either conclusion III or conclusion IV is correct' and Option D says 'Neither conclusion I nor conclusion II is correct'. Given that Conclusion I fails (bacteria and pathogens can be disjoint despite sharing microorganisms as superset), option D is valid. Option C relates to a separate premise set.