Question Details

Examine the following statements and accompanying conclusions. Even if they conflict with established knowledge, assume the statements to be factual. Evaluate the conclusions and determine which of them logically and definitely follows from the provided statements, ignoring general facts. Select the correct option:

Statements:
All Laptops are Computers.
Some Computers are Calculators.
All Calculators are Devices.

Conclusions:
I. Some Laptops are Calculators.
II. No Calculator is a Laptop.

Options

A

Both conclusions I and II follow

B

Only conclusion I follows

C

Either conclusion I or II follows

D

Neither conclusion I nor II follows

E

Only conclusion II follows

Show Answer

Correct Answer :

Option C

Either conclusion I or II follows

Solution :

Correct Answer: Either conclusion I or II follows

Step-by-Step Explanation:

Step 1: Analyze the Given Statements
Let us represent the given statements in terms of set relationships/Venn diagrams:
1. Statement 1: "All Laptops are Computers." (The set of Laptops is entirely inside the set of Computers.)
2. Statement 2: "Some Computers are Calculators." (There is an intersection between the set of Computers and the set of Calculators.)
3. Statement 3: "All Calculators are Devices." (The set of Calculators is entirely inside the set of Devices.)

Step 2: Evaluate the Individual Conclusions
Now, let us examine the relationship between Laptops and Calculators:
- Statement 1 tells us Laptops are a subset of Computers.
- Statement 2 tells us that Calculators overlap with Computers, but it does not specify whether this overlap includes Laptops or not.
- Therefore, there are two possibilities for the relationship between Laptops and Calculators:
1. The set of Calculators overlaps with the set of Laptops (Some Laptops are Calculators).
2. The set of Calculators has no overlap with the set of Laptops (No Calculator is a Laptop).

Since neither possibility is guaranteed on its own, neither Conclusion I ("Some Laptops are Calculators") nor Conclusion II ("No Calculator is a Laptop") definitely follows independently.

Step 3: Check for Complementary Pair (Either/Or Condition)
To determine if an "Either/Or" choice applies between Conclusion I and Conclusion II, we check the three rules for a complementary pair:
1. Both conclusions must have the same subject and predicate (Laptops and Calculators).
2. Both individual conclusions must be uncertain/indefinite.
3. One conclusion must be a Particular Positive statement ("Some Laptops are Calculators") and the other must be a Universal Negative statement ("No Calculator is a Laptop"). This forms a standard complementary pair (Some + No).

Since one of these two mutually exclusive conditions must be true in any possible Venn diagram scenario, either Conclusion I or Conclusion II must logically follow.

Conclusion:
Therefore, Either conclusion I or II follows.

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