If proposition 'some milk is curd' is taken to be true, then which of the following propositions can be false?
No milk is curd.
The statement 'Some milk is curd' is a particular affirmative proposition (I-type). On the traditional square of opposition, the I-proposition and the E-proposition ('No milk is curd', universal negative) are contradictories. Contradictories can never both be true and can never both be false — exactly one must be true and the other false. So if 'Some milk is curd' is TRUE, its contradictory 'No milk is curd' must be FALSE. Hence this is the proposition that is definitely false.
Checking the others: 'All milk is curd' (A-type) is the superaltern of the given I-proposition — the truth of I does not settle the truth of A, so it is undetermined (could be true or false), not necessarily false. 'Some curd is milk' is simply the converse of 'Some milk is curd'; conversion of an I-proposition is valid, so it is necessarily TRUE. 'Some milk is not curd' (O-type) is the subcontrary of the given I-proposition — subcontraries can both be true, so it too is undetermined. Only the universal negative is forced to be false.
Correct answer: No milk is curd.
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