Three statements are given, followed by three conclusions numbered I, II, and…
2023
Three statements are given, followed by three conclusions numbered I, II, and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: All pinks are scarlets.
Some scarlets are blues.
No blue is brown.
Conclusions: I. Some browns are blues. II. No pink is brown. III. Some scarlets are pinks.
- A.
Only conclusions II and III follow
- B.
Only conclusion I follows
- C.
Only conclusion III follows
- D.
Only conclusions I and II follow
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Correct answer: C
Given statements: All pinks are scarlets. Some scarlets are blues. No blue is brown.
Conclusion I — Some browns are blues: This does not follow. The premise "No blue is brown" states that blues and browns are disjoint, so you cannot infer that any brown is blue.
Conclusion II — No pink is brown: This does not follow. There is no statement preventing a pink from being brown (the premises do not state that scarlets or pinks cannot be brown). For example, it is consistent with the premises to have an object that is both pink and brown (and not blue).
Conclusion III — Some scarlets are pinks: This does not follow. "All pinks are scarlets" does not guarantee that any pinks exist. The premise "Some scarlets are blues" gives existence of some scarlets, but those need not be pink. A consistent situation is that there are scarlets (some of them blue) but no pinks at all.
Final conclusion: None of the three conclusions follow logically from the given statements.
Note: Since none of the provided answer choices state that none follow, all given options are incorrect.