Read the following statement carefully and identify the conclusion that follows. Statement: All actors are professionals. All professionals are creative. Some creative people are lazy. Conclusions: I. Some actors are lazy. II. All actors are creative.
- (a)Only I follows
- (b)Only II follows
- (c)Both I and II follow
- (d)Neither I nor II follows
Answer
Why
Correct — B.
Rule: All A are B + All B are C → All A are C.
A Some statement about C tells you nothing about A.
Actors sit inside professionals, and professionals inside creative people, so all actors are creative: II follows.
The lazy creative people may all be non-actors. Some actors are lazy is possible, not certain, so I does not follow → option (b).
Why the others are wrong
- (a)Only I follows — Some actors are lazy is only a possibility: the lazy group overlaps creative people, but nothing places that overlap among actors. This option also drops II, which is certain.
- (c)Both I and II follow — I fails: the lazy people are some of the creative ones, and those may all be outside the actors. II alone is forced by the two All statements.
- (d)Neither I nor II follows — II is certain: every actor is a professional and every professional is creative, so every actor is creative. 'Neither I nor II follows' throws away that definite conclusion.
Concept
Syllogisms are checked with nested circles. Draw actors inside professionals, and professionals inside creative.
Some creative people are lazy puts a lazy circle overlapping the creative one, but you may draw it outside the professionals entirely. A conclusion follows only if it holds in every such drawing.
II holds in every drawing. I holds in some and fails in others, so it does not follow.
Some actors being lazy is a possibility, and an item that phrased conclusion I that way would accept it. As printed, I is a definite claim, and a definite claim needs certainty.
Key facts
- All A are B and All B are C together give All A are C.
- Some C are D says nothing definite about A, a subset of C.
- A conclusion must hold in every possible diagram, not just one.
Study next
Common traps
- Carrying some down a chain of all statements, as if some creative people being lazy made some actors lazy
- Treating possible as follows: I could be true but is not certain
19 Sep 2024, 12:30, Reasoning Q.5 uses the same chain: all teachers are dancers, all dancers are engineers, some engineers are beautiful. Some dancers are beautiful fails there for the same reason (keyed Neither).
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