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 : 

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).

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.