Directions: In each of the following questions, two statements are given,…
2023
Directions: In each of the following questions, two statements are given, followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read the conclusions and decide which of them logically follows from the given statements, disregarding commonly known facts.
Statements:
Some musicians are not dancers.
Some dancers are actors.
Conclusions:
I. Some musicians are actors.
II. Some actors are not musicians.
- A.
Only conclusion I follows
- B.
Only conclusion II follows
- C.
Either conclusion I or conclusion II follows
- D.
Neither conclusion I nor conclusion II follows
- E.
Both conclusions I and II follow
Show answer & explanation
Correct answer: D
Concept: In syllogisms, a statement is either universal ('All A are B', 'No A is B') or particular ('Some A are B', 'Some A are not B'). A basic rule of valid syllogistic reasoning is that when BOTH given statements are particular, no definite conclusion connecting the two end terms can be drawn -- with two particular premises, more than one arrangement of the groups is logically possible, so no single conclusion is forced to hold in every case.
Application: Here, Statement 1 ('Some musicians are not dancers') is a particular statement, and Statement 2 ('Some dancers are actors') is also a particular statement. Both are particular, and they share only the term 'dancers' as the middle term linking musicians and actors. Because neither statement is universal, the relationship between musicians and actors is not fixed -- it can vary across different arrangements that are equally consistent with both statements.
Cross-check: Consider two different arrangements that both satisfy the given statements. (i) Let the dancer who is an actor be a person entirely separate from all musicians -- this still satisfies both statements, but here no musician is an actor, so Conclusion I fails in this arrangement. (ii) Let one musician also be the dancer who is an actor, and let this person be the only actor -- this again satisfies both statements, but here every actor is a musician, so Conclusion II fails in this arrangement. Since each conclusion fails in at least one arrangement consistent with the statements, neither is guaranteed to hold in every case.
Result: Therefore, neither conclusion I nor conclusion II necessarily follows from the given statements.