Each of the following questions presents a series of statements followed by two conclusions designated as I and II. You must accept the statements as true, even if they depart from established facts. Evaluate the conclusions and decide which one logically follows from the statements.
Statements:
All Tablet are Device.
All Device are Computer.
Some Laptop are Computer.
Conclusions:
I: All Tablet are Laptop
II: Some Tablet are not Laptop
Correct Answer :
If either conclusion I or II follows.
Solution :
Correct Answer: If either conclusion I or II follows.
Let us analyze the given statements and conclusions step-by-step using logical reasoning and set theory / Venn diagram concepts.
Given Statements:
1. All Tablet are Device.
2. All Device are Computer.
3. Some Laptop are Computer.
Analysis of Statements:
From Statement 1 ("All Tablet are Device") and Statement 2 ("All Device are Computer"), we can combine them to conclude:
This means the set of Tablets is completely contained within the set of Computers.
Statement 3 tells us that "Some Laptop are Computer", which means there is an intersection between the set of Laptops and the set of Computers. However, no specific relationship or direct link is given between the set of Tablets and the set of Laptops. Therefore, a Tablet may or may not be a Laptop.
Evaluating Conclusions:
Conclusion I: All Tablet are Laptop.
Conclusion II: Some Tablet are not Laptop.
Notice the relationship between Conclusion I and Conclusion II:
- Conclusion I is a universal affirmative statement (A-type): "All Tablet are Laptop".
- Conclusion II is a particular negative statement (O-type): "Some Tablet are not Laptop".
In classical logic, an A-type statement ("All A are B") and an O-type statement ("Some A are not B") form a complementary pair. They are exact contradictories of each other. Either all Tablets are Laptops, or there exists at least one Tablet that is not a Laptop (i.e., some Tablets are not Laptops). Both statements cannot be true at the same time, and both cannot be false at the same time.
Since the relation between Tablet and Laptop is uncertain from the given premises, either Conclusion I must be true, or Conclusion II must be true.
Therefore, either conclusion I or II follows.
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