In the following question, two statements are given each followed by two conclusions I and II. You have to consider the statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statements:
(I) All shawls are carpets.
(II) No carpet is a pullover.
Conclusion:
(I) No shawls are pullovers.
(II) All carpets are shawls.
- AConclusion I follows
- BConclusion II follows
- CNeither I nor II follows
- DBoth I and II follows
Solution & Step-by-step Explanation
Let's evaluate using set logic or Venn diagrams:
"All shawls are carpets" means the set of Shawls is completely contained inside the set of Carpets (Shawls⊆Carpets).
"No carpet is a pullover" means the set of Carpets and the set of Pullovers are entirely disjoint (Carpets∩Pullovers=∅).
Evaluating Conclusions:
Conclusion I: "No shawls are pullovers." Since all shawls lie inside carpets, and no part of carpets overlaps with pullovers, it is impossible for any shawl to be a pullover. Hence, this conclusion is definitely true and follows.
Conclusion II: "All carpets are shawls." This is a converse statement. We only know that all shawls are carpets, which does not necessarily mean all carpets are shawls (there could be carpets that are not shawls). Hence, this conclusion does not follow.
Thus, only conclusion I follows.
"All shawls are carpets" means the set of Shawls is completely contained inside the set of Carpets (Shawls⊆Carpets).
"No carpet is a pullover" means the set of Carpets and the set of Pullovers are entirely disjoint (Carpets∩Pullovers=∅).
Evaluating Conclusions:
Conclusion I: "No shawls are pullovers." Since all shawls lie inside carpets, and no part of carpets overlaps with pullovers, it is impossible for any shawl to be a pullover. Hence, this conclusion is definitely true and follows.
Conclusion II: "All carpets are shawls." This is a converse statement. We only know that all shawls are carpets, which does not necessarily mean all carpets are shawls (there could be carpets that are not shawls). Hence, this conclusion does not follow.
Thus, only conclusion I follows.