Three statements are given followed by three conclusions numbered I, II and III.
Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
No card is a parcel.
All cards are envelopes. Some envelopes are bags.
Conclusions:
I. All envelopes can never be parcels.
II. No card is a bag.
III. At least some bags are postcards.
Correct Answer :
Only I follows
Solution :
To determine which of the conclusions logically follow from the given statements, let us analyze the relationships between the terms step-by-step:
Step 1: Analyze the Statements
1. No card is a parcel: This means the set of "cards" and the set of "parcels" are completely disjoint. There is no overlap between them.
2. All cards are envelopes: This means the entire set of "cards" lies inside the set of "envelopes".
3. Some envelopes are bags: This means there is an intersection between the set of "envelopes" and the set of "bags".
Step 2: Evaluate the Conclusions
Conclusion I: All envelopes can never be parcels.
- From Statement 2, we know that all "cards" are a part of "envelopes".
- From Statement 1, we know that no "card" can be a "parcel".
- Therefore, the portion of "envelopes" that consists of "cards" can never be "parcels". Since a part of "envelopes" (the cards) can never be "parcels", it is impossible for all "envelopes" to be "parcels".
- Thus, "All envelopes can never be parcels" is definitely true. This conclusion follows.
Conclusion II: No card is a bag.
- We are given that all cards are envelopes, and some envelopes are bags.
- There is no direct information restricting the relationship between "cards" and "bags". They may or may not overlap.
- Since this is not a definite relationship, this conclusion does not follow.
Conclusion III: At least some bags are postcards.
- The term "postcards" is not mentioned or defined in the statements.
- Therefore, no logical conclusion can be drawn about "postcards". This conclusion does not follow.
Conclusion:
Only Conclusion I logically follows from the statements.
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