If the proposition- ‘Some frogs are not mammals.' is given as false, then which of the following propositions can be immediately inferred to be false? 

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UGC NET Paper 1: Held on 28th Feb 2023 Shift 2
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  1. Some frogs are mammals. 
  2. All non-frogs are mammals. 
  3. No frogs are mammals. 
  4. All frogs are mammals. 

Answer (Detailed Solution Below)

Option 3 : No frogs are mammals. 
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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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If the proposition "Some frogs are not mammals" is given as false, then the following proposition can be immediately inferred to be false: No frogs are mammals.

Important Points

  • This is because if "Some frogs are not mammals" is false, it means that there are no frogs that are not mammals, or in other words, all frogs are mammals.
  • The proposition "No frogs are mammals" directly contradicts this by asserting that there are no frogs that are mammals.
  • Therefore, if "Some frogs are not mammals" is false, then "No frogs are mammals" must also be false.
  • The truth values of the other options cannot be immediately determined solely based on the given information, as they are not directly related to the proposition "Some frogs are not mammals."
  • Additional information or logical reasoning would be required to determine the truth values of those propositions.

Hence,  No frogs are mammals is the correct answer.

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