Two Statements are given followed by two Conclusions : Statements : All cats are dogs. All cats are black. Conclusion-I : All dogs are black. Conclusion-II : Some dogs are not black. Which of the above Conclusions logically follows/follow from the two given Statements, disregarding commonly known facts?

(a) Only Conclusion-I
(b) Only Conclusion-II
(c) Neither Conclusion-I nor Conclusion-II ✓ UPSC's answer
(d) Both Conclusion-I and Conclusion-II

Why the answer is (c)

• The first statement 'All cats are dogs' establishes that the set of cats is a subset of the set of dogs, but it does not imply that all dogs are cats or that all dogs share the properties of cats.

• The second statement 'All cats are black' establishes that the set of cats is a subset of the set of black things.

• Combining these, we know that all cats are both dogs and black, but there is no information about dogs that are not cats.

• Conclusion-I 'All dogs are black' is invalid because dogs that are not cats may or may not be black; the premises do not restrict the color of non-cat dogs.

• Conclusion-II 'Some dogs are not black' is also invalid because it is possible that all dogs are cats (in which case all dogs would be black), so we cannot definitively conclude that some dogs are not black.

• Since neither conclusion can be logically deduced with certainty from the given statements, the correct answer is that neither follows.

Why the other options are wrong

(a) Only Conclusion-I: Conclusion-I is invalid because the premises do not state that all dogs are cats, so non-cat dogs might not be black.
(b) Only Conclusion-II: Conclusion-II is invalid because it is possible that all dogs are cats, which would mean all dogs are black, making the statement 'some dogs are not black' false.
(d) Both Conclusion-I and Conclusion-II: Both conclusions are invalid for the reasons stated above; neither can be logically derived from the premises.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.