Consider the following Statements and Conclusions : Statements : 1. Some rats are cats. 2. Some cats are dogs. 3. No dog is a cow. Conclusions : I. No cow is a cat. II. No dog is a rat. III. Some cats are rats. Which of the above conclusions is/are drawn from the statements ?

(a) I, II and III
(b) Only I and II
(c) Only III ✓ UPSC's answer
(d) Only II and III

Why the answer is (c)

• Statement 1 states 'Some rats are cats', which logically implies 'Some cats are rats' (converse), making Conclusion III valid.

• Statement 2 states 'Some cats are dogs', but this does not establish any relationship between cats and cows, so Conclusion I ('No cow is a cat') cannot be definitively drawn.

• Statements 1 and 2 link rats to cats and cats to dogs, but there is no direct or indirect logical link proving that no dog is a rat, so Conclusion II is not necessarily true.

• Since only Conclusion III is logically derived from the given statements, option (c) is the correct answer.

Why the other options are wrong

(a) I, II and III: Conclusions I and II are not logically valid inferences from the given statements.
(b) Only I and II: Conclusions I and II are not logically valid inferences from the given statements.
(d) Only II and III: Conclusion II is not a logically valid inference from the given statements.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.