Question

Read the given statements and conclusions carefully, assuming the information given is true. Decide which of the conclusions logically follows from the statements.
Statements:
No keyboard is a mouse. All mouses are computers. All computers are laptops.
Conclusions:
I. All mouses are laptops.
II. All computers can never be keyboards.

• A. Only conclusion I follows
• B. Only conclusion II follows
• C. Neither conclusion I nor II follows
• D. Both conclusions I and II follow

Answer 1

The Correct Option is D

To determine which conclusions logically follow from the given statements, let's first summarize and analyze the statements using logical reasoning:
Statements:
1. No keyboard is a mouse.
2. All mouses are computers.
3. All computers are laptops.

Analyzing Statements:

• From Statement 2: "All mouses are computers," it follows that every mouse is also a computer.
• From Statement 3: "All computers are laptops," it logically follows that every computer is a laptop.
• Connecting these, we infer: "All mouses are laptops," since mouses are a subset of computers, which are a subset of laptops.

Conclusions:

• I. All mouses are laptops. This conclusion directly follows from the combined inferences of Statements 2 and 3.
• II. All computers can never be keyboards. Since "No keyboard is a mouse" and "All mouses are computers," it means a computer cannot be a keyboard because it contains mouses, which keyboards cannot contain.

Conclusion:
Both conclusions I and II logically follow from the given statements as they are consistent with the deductions we derived. Therefore, the correct option is “Both conclusions I and II follow.”

Answer 2

Based on the given statements, both conclusions I and II follow logically.

Additional Context:

• Statements Analysis:
  • 1. No keyboard is a mouse → Keyboard and mouse are mutually exclusive
  • 2. All mouses are computers → Mouse is a subset of computers
  • 3. All computers are laptops → Computer is a subset of laptops
• Conclusion I Evaluation:
  • "All mouses are laptops"
    • From statements 2 and 3: Mouse → Computer → Laptop
    • Thus, Mouse → Laptop (by transitive property)
    • Follows
• Conclusion II Evaluation:
  • "All computers can never be keyboards"
    • From statement 1: No keyboard is mouse
    • From statement 2: All mouses are computers
    • Thus, some computers (mouses) are definitely not keyboards
    • Plus, other computers may or may not be keyboards (not specified)
    • The word "never" makes this conclusion too absolute
• Revised Analysis:
  • Actually, Conclusion II is also correct because:
    • If all computers were keyboards, it would violate statement 1 (since some computers are mouses)
    • Thus, it's impossible for all computers to be keyboards
    • Therefore "All computers can never be keyboards" is correct
• Venn Diagram Representation:
  • Keyboard circle does not intersect with Mouse circle
  • Mouse circle entirely within Computer circle
  • Computer circle entirely within Laptop circle
• Logical Flow:
  • Mouse ⊂ Computer ⊂ Laptop
  • Keyboard ∩ Mouse = ∅
  • Thus Keyboard cannot encompass all Computers

Correct Answer: (4) Both conclusions I and II follow.