Which one of the following propositions is logically equivalent to the proposition-"Some attorneys are logicians"? 

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UGC NET Paper 1: Held on 1st Mar 2023 Shift 2
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  1. Some logicians are not attorneys.
  2. Some attorneys are non-logicians.
  3. Some logicians are attorneys.
  4. Some non-logicians are non-attorneys.

Answer (Detailed Solution Below)

Option 3 : Some logicians are attorneys.
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UGC NET Paper 1: Held on 21st August 2024 Shift 1
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Detailed Solution

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Key Points 
  • The proposition "Some attorneys are logicians" means that there exists at least one attorney who is also a logician.
  • This means that the set of attorneys is a subset of the set of logicians.
  • Therefore, some logicians must be attorneys. This is equivalent to proposition 3.
  • Proposition 1 is not logically equivalent because it says that there exist logicians who are not attorneys. This is not necessarily true, as it is possible that all logicians are also attorneys.
  • Proposition 2 is not logically equivalent because it says that some attorneys are not logicians. This is not necessarily true, as it is possible that all attorneys are also logicians.
  • Proposition 4 is not logically equivalent because it says that some non-logicians are not attorneys. This is not necessarily true, as it is possible that some non-logicians are also attorneys.
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