Directions: In the question below, some statements are given followed by two conclusions. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions definitely follows from the given statements, disregarding commonly known facts.
Statements:
All laptops are devices
Some devices are portable
Only portable items are handhelds
Conclusions:
I. No laptop is a handheld
II. All portable items being devices is a possibility
Correct Answer :
Both conclusions I and II follow
Solution :
The correct option is Both conclusions I and II follow.
Let us analyze the given statements step-by-step:
Step 1: Understanding the Statements
1. All laptops are devices: The set of laptops is completely contained within the set of devices.
2. Some devices are portable: There is an intersection between the set of devices and the set of portable items.
3. Only portable items are handhelds: In logic, a statement of the form "Only A are B" means "All B are A", accompanied by an exclusivity rule. Thus, "All handhelds are portable items", and handhelds cannot overlap with any category outside of portable items.
Step 2: Evaluating Conclusion I
Conclusion I: No laptop is a handheld
Since handhelds are exclusively restricted to being portable items, handhelds cannot be laptops. Therefore, "No laptop is a handheld" definitely follows from the given statements.
Step 3: Evaluating Conclusion II
Conclusion II: All portable items being devices is a possibility
From Statement 2, we know that "Some devices are portable". A "some" relationship allows for the possibility that all portable items are contained within devices, as there is no negative constraint prohibiting it. Therefore, "All portable items being devices is a possibility" is a valid potential case and definitely follows.
Final Verdict:
Both Conclusion I and Conclusion II logically follow from the statements.
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