In the following question below are given some statements followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusion logically follows the given statements. Statements: I. Some pens are pencils. II. Some pencils are cups. Conclusions: I. Some cups are pens. II. Some pencils are pens.
In the following question below are given some statements followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. Some pens are pencils.
II. Some pencils are cups.
Conclusions:
I. Some cups are pens.
II. Some pencils are pens.
correct answer is: option b (II)[Only conclusion (II) follows.]
Explanation: Let's analyze the statements using a Venn diagram. Statement I says "Some pens are pencils," meaning there's an overlap between the set of pens and the set of pencils. Statement II says "Some pencils are cups," meaning there's an overlap between the set of pencils and the set of cups. Conclusion I, "Some cups are pens," is not necessarily true. The cups and pens might not overlap. Conclusion II, "Some pencils are pens," is directly derived from statement I ("Some pens are pencils"). If some pens are pencils, then it's logically true that some pencils are pens.
- Option a: This is incorrect because conclusion I does not necessarily follow. There's no guaranteed overlap between cups and pens.
- Option b: This is the correct answer. Conclusion II directly follows from statement I.
- Option c: This is incorrect because only conclusion II follows. Conclusion I is not necessarily true.
- Option d: This is incorrect because conclusion II does follow logically from the given statements.
