Statements: 1. Most CPUs are keyboards. 2. No keyboard is a Mouse. 3. All…
2024
Statements:
1. Most CPUs are keyboards.
2. No keyboard is a Mouse.
3. All Mouses are CPU.
Conclusions:
I. Some keyboards are CPU.
II. All CPUs are Mouse.
III. No Mouse is a keyboard.
IV. Some Mouse are keyboard.
- A.
Only I follows
- B.
Only II and III follow
- C.
Only I and III follow
- D.
Only II follows
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept: A categorical statement can be reversed (subject and predicate swapped) only according to fixed conversion rules: a “most/some” (particular) statement reverses into another particular statement; a “no” (universal negative) statement reverses into another universal negative -- it holds identically in both directions; an “all” (universal affirmative) statement reverses only into a weaker particular statement, never into another “all” statement.
Application: Applying these rules to each of the three given statements:
Statement | Type | Valid reverse reading | Effect on the conclusions |
|---|---|---|---|
Most CPUs are keyboards | Particular (“most” implies “some”) | Some keyboards are CPUs | Matches conclusion I |
No keyboard is a Mouse | Universal negative | No Mouse is a keyboard | Matches conclusion III |
All Mouses are CPU | Universal affirmative | Only “Some CPUs are Mouse” (never the full reverse) | Conclusion II, which claims the full reverse, does not hold |
Conclusion IV (“Some Mouse are keyboard”) directly contradicts the second statement, which rules out any overlap between keyboard and Mouse in either direction, so it cannot hold either.
Cross-check: A single Venn diagram can satisfy all three statements at once: draw Mouse as a circle entirely inside CPU, and draw keyboard as a circle overlapping most of CPU while staying completely separate from Mouse. This layout keeps keyboard and CPU overlapping (supporting conclusion I), keeps Mouse and keyboard fully apart (supporting conclusion III), and keeps a slice of CPU (the keyboard-only part) outside Mouse (so conclusion II's full-reverse claim fails).
Result: Only conclusions I and III are validly derivable from the given statements.