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: Some rats are mouse. No mouse is a rodent. Some rats are kittens. Conclusions: I. No rodent is a kitten. II. Some rats are rodent. III. No kitten is a mouse.

Correct — B.

Rule: a conclusion follows only if it holds in every arrangement the statements allow.

I fails. Nothing in the statements links rodents to kittens, so a rat that is a kitten may also be a rodent.

II fails. 'No mouse is a rodent' rules out only the rats that are mice. The remaining rats may all avoid rodents entirely.

III fails. Kittens and mice each overlap rats, and nothing keeps those two overlaps apart, so some kitten may be a mouse.

Not one of the three is forced, which is option (b).

Why the others are wrong

• (a)
  Only conclusion I follows — I would need rodents and kittens kept apart, but no statement mentions both. Where two terms never meet, a negative conclusion is not forced.
• (c)
  Only conclusion III follows — III would need kittens and mice separated. Each is tied to rats only by 'some', and two overlapping parts of rats may share members.
• (d)
  Only conclusion II follows — II reads 'no mouse is a rodent' as proof that the other rats are rodents. Ruling one class out never rules another class in.

A syllogism is settled by asking whether the conclusion can be made false while every statement stays true. If one such arrangement exists, the conclusion does not follow.

A some statement gives an overlap, and two overlaps with the same class may or may not coincide. That is why III fails.

A no statement removes a link, and removing one link never creates another. That is why II fails.

Where two terms share no statement at all, as rodents and kittens do here, nothing whatever follows about them.

Key facts

• A conclusion follows only if it is true in every diagram consistent with the statements.
• Two classes each overlapping a third may still overlap each other, so a pair of 'some' statements forces no negative conclusion.
• A universal negative between two classes says nothing about a third class.

Common traps

• Using real biology, in which mice are rodents, instead of the statements as printed
• Reading 'no mouse is a rodent' as evidence that some rats are rodents
• Assuming two classes must be separate merely because no statement joins them

No directly related past PYQ was found.