Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusion(s) logically follow(s) from the statements. Statements: Some eagles are sparrows. All sparrows are parrots. No parrot is a penguin. Conclusions: (I) Some parrots are eagles. (II) No penguin is a sparrow.
- (a)Only conclusion I follows.
- (b)Only conclusion II follows.
- (c)Both conclusions I and II follow.
- (d)Neither conclusion I nor II follows.
Answer
Why
Correct — C. Take the three statements as given, whatever they say about real birds.
Rule: a definite overlap can be carried through an all-statement, and a total exclusion passes down to everything inside the excluded class.
Conclusion I: some eagles are sparrows, so at least one bird is both. All sparrows are parrots, so that same bird is a parrot too. It is a parrot that is an eagle, so some parrots are eagles.
Conclusion II: all sparrows lie inside parrots and no parrot is a penguin, so no sparrow can be a penguin. Turned round, no penguin is a sparrow.
Both conclusions stand, which is option (c).
Why the others are wrong
- (a)Only conclusion I follows. — This stops after the overlap and misses that the ban on parrots being penguins passes down to sparrows, every one of which is a parrot.
- (b)Only conclusion II follows. — This drops the eagle-sparrow overlap. Some eagles are sparrows is a definite statement, and it converts, so those sparrows are eagles and they are all parrots.
- (d)Neither conclusion I nor II follows. — Rejecting both discards two valid chains. Neither conclusion needs an assumption beyond the three statements printed.
Concept
Syllogism items are decided by the diagram the statements force, not by ornithology.
Some eagles are sparrows guarantees a shared region. All sparrows are parrots pushes that whole region inside parrots. No parrot is a penguin cuts parrots off from penguins entirely.
Two standard conversions settle most items of this shape. A some-statement converts, so some A are B gives some B are A. A universal negative converts too, so no A is B gives no B is A.
The stem's warning that the statements may be at variance with commonly known facts is an instruction, not decoration: sparrows being parrots is exactly the sort of thing you are meant to accept for the length of the question.
Key facts
- Some A are B always converts to some B are A.
- No A is B always converts to no B is A.
- All A are B combined with no B is C gives no A is C.
Study next
Common traps
- Rejecting a conclusion because it contradicts what you know about real birds
- Treating some eagles are sparrows as one-directional and refusing to convert it
- Assuming a negative statement blocks every inference that follows it
Read the two conclusions separately and score each on its own; a set is 'both follow' only when neither needs an assumption from outside the statements.
A two-conclusion version carrying the same variance warning is at 10 Sep 2024, 09:00, Reasoning Q.1.
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