Read the given statements and conclusions carefully assuming that the information given in the statements is true, even if it appears to be at variance with com monly known facts. Decide which of the given conclusion(s) logically follows from the statements. Statements:
No keyboard is a mouse.
- All mouses are computers.
- All computers are laptops.
Conclusions:
1. All mouses are laptops.
2. All computers can never be keyboards.
Correct Answer :
Both conclusions I and II follow
Solution :
The correct option is: Both conclusions I and II follow.
Let us analyze the given statements step-by-step using logical reasoning to understand why both conclusions are correct.
Analysis of Statements:
1. "No keyboard is a mouse": This means that the set of keyboards and the set of mouses are completely disjoint. There is no overlap between them.
2. "All mouses are computers": The entire set of mouses is contained within the set of computers.
3. "All computers are laptops": The entire set of computers is contained within the set of laptops.
Evaluating Conclusion 1: "All mouses are laptops"
We are given that all mouses are computers, and all computers are laptops.
Since the entire group of mouses lies inside the group of computers, and the entire group of computers lies inside the group of laptops, it logically follows that all mouses are inside the group of laptops.
Therefore, conclusion 1 follows.
Evaluating Conclusion 2: "All computers can never be keyboards"
The phrase "All computers can never be keyboards" means it is impossible for all computers to be keyboards (i.e., the set of computers can never be completely inside the set of keyboards).
We know that all mouses are computers. This means that a part of the computers consists of mouses.
We also know that no mouse is a keyboard. Since all mouses are computers, the "mouse" portion of the computers can never overlap with keyboards.
Because there is a portion of computers (specifically, all mouses) that can never be keyboards, it is impossible for the entire set of computers to be keyboards.
Therefore, conclusion 2 follows.
Since both conclusion 1 and conclusion 2 logically follow from the statements, the correct choice is indeed Both conclusions I and II follow.
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