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.

Updated On: Mar 28, 2025
  • Only conclusion I follows
  • Only conclusion II follows
  • Neither conclusion I nor II follows
  • Both conclusions I and II follow
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The Correct Option is D

Solution and Explanation

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.

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