RAS question
Statements: All roses are flowers. Some flowers are red. Conclusions: I. Some roses are red. II. Some red things are flowers. Which conclusion(s) follow?
Correct answer: (C) Only Conclusion II follows.
Only Conclusion II follows: from the statement that some flowers are red, it necessarily follows that some red things are flowers, but it does not necessarily follow that some roses are red.
Explanation
The two statements have to be read as set relations. NCERT defines a subset as a set whose every element is also an element of another set, so "all roses are flowers" only places roses inside the wider set of flowers. NCERT also defines intersection as the elements common to two sets; "some flowers are red" says that the set of flowers intersects the set of red things. That same intersection can be stated as "some red things are flowers", so Conclusion II follows. But the red flowers need not lie inside the rose subset. They may be any other flowers, so Conclusion I is not a necessary conclusion.
Why the other options are wrong
- (A) It wrongly accepts Conclusion I, even though the red flowers mentioned in the statement need not include any roses.
- (B) It wrongly accepts Conclusion I and rejects Conclusion II, although the statement "some flowers are red" directly gives "some red things are flowers" by conversion.
- (D) It wrongly rejects Conclusion II, which follows because the same flower-red overlap can be read from either side.
Concept
This tests categorical syllogism through basic set relations: subset for "all" and intersection for "some". It recurs in RAS reasoning because small wording changes decide whether a conclusion is necessary or only possible.