RAS question
Statements: Some books are pens. Some pens are erasers. Conclusions: I. Some books are erasers. II. No book is an eraser. Which conclusion(s) follow?
Correct answer: (D) Either Conclusion I or II follows.
From the statements 'Some books are pens' and 'Some pens are erasers', neither conclusion follows individually, but either 'Some books are erasers' or 'No book is an eraser' must follow.
Explanation
The two given premises are particular affirmative statements joined through the middle term 'pens'. NCERT frames deductive reasoning as drawing a conclusion from premises that are assumed to be true, and also stresses that statements involving 'all' or 'some' need careful handling when their negations are considered. Here, the premises only prove that some books fall inside pens and some erasers fall inside pens; they do not fix any relationship between books and erasers. So Conclusion I is not individually certain, and Conclusion II is not individually certain either. However, the two conclusions are complementary for the book-eraser relation: either at least one book is an eraser, or no book is an eraser. Therefore, the valid choice is 'Either Conclusion I or II follows'.
Why the other options are wrong
- (A) Both conclusions cannot be asserted together because 'some books are erasers' and 'no book is an eraser' are complementary claims about the same book-eraser relation.
- (B) Conclusion I overreaches because the shared middle term 'pens' does not prove that the books which are pens overlap with the pens which are erasers.
- (C) Conclusion II also overreaches because the premises do not rule out an overlap between books and erasers; they simply leave that relationship undecided.
Concept
This tests syllogistic reasoning with particular affirmative statements and complementary conclusions. It recurs in RAS reasoning because the exam often checks whether candidates distinguish a definite conclusion from an exhaustive either-or case.