In classical square of opposition if 'No S is P’ is given as false then which of the following could be immediately inferred from it?

(A) ‘Some S is not P’ is true

(B) ‘All S is P’ is undetermined

(C) ‘Some S is not P’ is undetermined

(D) ‘Some S is P’ is true

(E) ‘Some S is not P’ is false

Choose the correct answer from the options given below : 

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UGC NET Paper 1: Held on 9th July 2022 Shift 1
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  1. (B), (D) and (E) only 
  2. (A), (B) and (D) only  
  3. (A), (D) and (E) only 
  4. (B), (C) and (D) only 

Answer (Detailed Solution Below)

Option 4 : (B), (C) and (D) only 
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Detailed Solution

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The correct answer is (B), (C) and (D) only.

Important Points 

The classical square of opposition is a diagram that illustrates the relationships between four basic types of categorical propositions: A (All S is P), E (No S is P), I (Some S is P), and O (Some S is not P).

F1 A.A. Madhu 19.05.20 D1

The classical square of opposition consists of four standard categorical propositions:

  • Universal Affirmative (A): All S is P.
  • Universal Negative (E): No S is P.
  • Particular Affirmative (I): Some S is P.
  • Particular Negative (O): Some S is not P.

When "No S is P" is given as false, it means that at least some S is P, which means that "Some S is P" is true. Therefore, option (D) "Some S is P is true" is a valid inference.

Key Points

(A) "Some S is not P" is true:

  • We cannot infer this from the information given because the falsity of "No S is P" does not necessarily mean that "Some S is not P" is true.
  • It only means that there is at least some overlap between S and P.

(B) "All S is P" is undetermined:

  • This is a valid inference.
  • The falsity of "No S is P" doesn't provide information about whether "All S is P" is true or false.
  • It leaves this proposition undetermined.

(C) "Some S is not P" is undetermined:

  • This is also a valid inference for the same reason as option (B).

(E) "Some S is not P" is false:

  • We cannot conclude this from the given information.
  • The falsity of "No S is P" means there is some overlap between S and P, but it doesn't tell us if "Some S is not P" is false.

So, the correct answer is (B), (C), and (D), as these can be immediately inferred from the given information.

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