Statements: All cats are dogs. No dog is a rat. Conclusions: I. No cat is a rat. II. Some rats are cats. Which conclusions follow?
Only I follows. Every cat is inside the dogs circle, and the dogs circle shares nothing with rats, so no cat can be a rat. II contradicts I, so it cannot follow.
Explain it simply
"All" followed by "No" is one of the few patterns that always gives a definite conclusion. If a small circle sits completely inside a bigger circle, and the bigger circle is completely separate from a third circle, then the small circle is separate from the third as well. Think of it as a hostel block inside a campus that is fenced off from the town.
Example
Statements: All cats are dogs. No dog is a rat.
[ Dogs ( Cats ) ] [ Rats ]- Cats lie entirely within Dogs.
- Dogs and Rats do not overlap at all.
- So Cats and Rats do not overlap. I (no cat is a rat) follows.
- II says some rats are cats, which is impossible once I is certain. II does not follow.
Answer: only I follows.
Also valid here: "Some dogs are not rats" (indeed all dogs are not rats) and "No rat is a cat" (the converse of I).
Pattern summary: All A are B + No B is C gives No A is C.
What to say in the interview
"Cats are wholly inside dogs, and dogs are wholly separate from rats, so no cat can be a rat. Conclusion I follows. II contradicts it, so only I."
Common mistakes
- Saying 'No cat is a rat' only 'probably' follows; this pattern is certain.
- Thinking 'No A is B' and 'No B is A' are different; they are equivalent.