Question:
Statement 1: All libraries are laboratories.
Statement 2: No laboratories are hostels.
Conclusions:
(a) All laboratories are libraries
(b) Some hostels are libraries
(c) Some libraries are hostels
(d) No library is a hostel
Statement 1: All libraries are laboratories.
Statement 2: No laboratories are hostels.
Conclusions: (a) All laboratories are libraries
(b) Some hostels are libraries
(c) Some libraries are hostels
(d) No library is a hostel
Statement 2: No laboratories are hostels.
Conclusions: (a) All laboratories are libraries
(b) Some hostels are libraries
(c) Some libraries are hostels
(d) No library is a hostel
Show Hint
If A ⊂ B and B is disjoint from C, then A is also disjoint from C.
Updated On: Aug 11, 2025
- Only (a) and (b)
- Only (b) and (c)
- Only (c) and (d)
- Only (d)
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The Correct Option is D
Solution and Explanation
Step 1: Translate the statements
- All libraries $\rightarrow$ laboratories
- No laboratories $\rightarrow$ hostels
Step 2: Analyze implications
Since all libraries are laboratories, and no laboratories are hostels, therefore: No library is a hostel.
(a) All laboratories are libraries — Converse of Statement 1, not valid.
(b) Some hostels are libraries — Contradicted by Statement 2.
(c) Some libraries are hostels — Contradicted.
(d) No library is a hostel — Correct inference.
% Final Answer \[ \boxed{\text{Only (d)}} \]
Since all libraries are laboratories, and no laboratories are hostels, therefore: No library is a hostel.
(a) All laboratories are libraries — Converse of Statement 1, not valid.
(b) Some hostels are libraries — Contradicted by Statement 2.
(c) Some libraries are hostels — Contradicted.
(d) No library is a hostel — Correct inference.
% Final Answer \[ \boxed{\text{Only (d)}} \]
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