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 Option: Either conclusion I or II follows

Let us analyze the given statements step-by-step using logical deductions and Venn diagrams concept:

Given Statements:
1. All Laptops are Computers.
2. Some Computers are Calculators.
3. All Calculators are Devices.

Analyzing the relationship between Laptops and Calculators:
From Statement 1, the set of Laptops is entirely contained within the set of Computers.
From Statement 2, there is an intersection between the set of Computers and the set of Calculators.
However, no direct connection or definite relationship is specified between Laptops and Calculators in the given statements. Therefore, any definite statement about the relation between Laptops and Calculators cannot be definitively concluded as true on its own.

Evaluating the Conclusions:

Conclusion I: "Some Laptops are Calculators." (Particular Positive)
Since no direct relation between Laptops and Calculators is given, this conclusion is not definitely true on its own.

Conclusion II: "No Calculator is a Laptop." (Universal Negative)
Similarly, since no direct negative relation is specified between Calculators and Laptops, this conclusion is also not definitely true on its own.

Complementary Pair Analysis (Either-Or Case):
Notice that conclusions I and II form a complementary pair because:
1. Both conclusions involve the same subject and predicate terms (Laptops and Calculators).
2. Both conclusions are individually doubtful/uncertain.
3. One conclusion is a Particular Positive statement ("Some Laptops are Calculators") and the other is a Universal Negative statement ("No Calculator is a Laptop").
Since both statements cannot be simultaneously false (either there is at least one Laptop that is a Calculator, or there is no Laptop that is a Calculator), exactly one of them must be true.

Therefore, Either conclusion I or II follows.

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