In the question below are given three statements followed by three conclusions…
2025
In the question below are given three statements followed by three conclusions numbered I, II and III. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements: I. All Men are Good II. Some Boys are Bad III. Few Bad is Good
Conclusions: I. Some boys are not bad II. Some men are good III. Some bad are not good
- A.
Only conclusion I follows
- B.
Only conclusion II follows
- C.
Only conclusion III follows
- D.
Both conclusion II and III follow
- E.
None of the conclusion follows
Attempted by 4 students.
Show answer & explanation
Correct answer: B
CONCEPT:
In categorical syllogism, a universal affirmative ('All A are B') always licenses the weaker particular claim about the same subject ('Some A are B') by subalternation, assuming the subject class is non-empty (the standard existential-import assumption used in these problems) -- the universal statement cannot be true unless at least some members exist that satisfy it. A particular affirmative ('Some A are B', which 'few A are B' is treated the same as) never licenses a particular-negative claim about the same two terms ('Some A are not B'), because a diagram where the ENTIRE A lies inside B remains fully consistent with 'Some A are B'. A conclusion counts as logically following only if it holds in EVERY diagram consistent with the given statements, not merely one.
APPLICATION:
The statements translate to: All Men are Good (Men entirely inside Good); Some Boys are Bad (Boys and Bad overlap); Few Bad is Good, i.e. Some Bad are Good (Bad and Good overlap).
Conclusion I, 'Some boys are not bad', would require boys guaranteed outside Bad -- but a diagram with the whole Boys set inside Bad still satisfies 'Some Boys are Bad', so this is not certain.
Conclusion II, 'Some men are good', follows directly by subalternation: since All Men are Good, at least some Men are Good in every consistent diagram.
Conclusion III, 'Some bad are not good', would require part of Bad guaranteed outside Good -- but a diagram with the whole Bad set inside Good still satisfies 'Few Bad is Good', so this is not certain.
CROSS-CHECK:
Draw one diagram with Boys entirely inside Bad, and Bad entirely inside Good, with Men entirely inside Good -- every given statement holds. In this diagram, 'some boys are not bad' is false and 'some bad are not good' is false, while 'some men are good' remains true purely because Men lies inside Good. Since a single consistent diagram already breaks conclusions I and III while conclusion II survives in every diagram, only conclusion II is a definite conclusion.
Result:
Only conclusion II follows.