Directions: Analyze the set of statements provided below and determine which of the conclusions logically follows, even if they contradict widely accepted facts.
Statements:
Only a few Cameras are Laptops
Some Watches are Backpacks
No Laptops are Backpacks
Conclusions:
I. Some Cameras are not Backpacks
II. All Cameras can never be Watches
Correct Answer :
If only conclusion I follows
Solution :
Correct Answer: If only conclusion I follows
Step-by-Step Explanation:
1. Breakdown of Given Statements:
- Statement 1: "Only a few Cameras are Laptops"
The phrase "Only a few" translates to two definite facts:
(i) Some Cameras are Laptops.
(ii) Some Cameras are NOT Laptops.
This means there exists a specific portion of Cameras that overlap with Laptops.
- Statement 2: "Some Watches are Backpacks"
This means there is an intersection between the set of Watches and the set of Backpacks.
- Statement 3: "No Laptops are Backpacks"
This means the set of Laptops and the set of Backpacks are completely disjoint (they have 0 overlap).
2. Evaluating Conclusion I: "Some Cameras are not Backpacks"
- From Statement 1, we know that a portion of Cameras are Laptops.
- From Statement 3, we know that no Laptops can ever be Backpacks.
- Therefore, the specific Cameras that are Laptops can never be Backpacks.
- This proves beyond doubt that at least some Cameras (the ones that are Laptops) are definitely not Backpacks.
- Thus, Conclusion I logically follows.
3. Evaluating Conclusion II: "All Cameras can never be Watches"
- "Can never be" implies a definite impossibility (i.e., it claims that it is impossible for all Cameras to be Watches).
- Looking at the statements, there is no direct or indirect restriction between Cameras and Watches.
- It is entirely possible for all Cameras to be inside the set of Watches without violating any given statements.
- Since it is possible for all Cameras to be Watches, the claim that they "can never be Watches" is false.
- Thus, Conclusion II does not follow.
Final Verdict:
Only Conclusion I logically follows from the given statements. Therefore, the correct choice is If only conclusion I follows.
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