If 'No S is P' is a false statement, then which of these statements is necessarily true ?

The correct answer is (B) Some S is P.

• Logical Principle: According to Aristotle's Square of Opposition in traditional logic, the universal negative proposition 'No S is P' (Type E) and the particular affirmative proposition 'Some S is P' (Type I) are contradictory statements. Two propositions are contradictory if they cannot both be true and they cannot both be false at the same time.
• Step-by-Step Deduction: The question states that the proposition 'No S is P' (Type E) is false. Since contradictory statements must have opposite truth values, the negation of a false proposition must be true. Therefore, its contradictory proposition 'Some S is P' (Type I) is necessarily true.
• Option Analysis and Verification: Option (A) 'All S is P' (Type A) is false because if 'No S is P' is false, some elements must overlap. Option (C) 'Some S is not P' (Type O) is the subalternate of the false E proposition, so its truth value remains undetermined (doubtful) directly from the falsity of E. Thus, Option (B) is the only definitively true statement.