If the proposition "Students are serious" is taken to be false, then which of the following propositions can be true?

Taking "All students are serious" as false makes its contradictory, Statement 3 (Some students are not serious), necessarily true.

The stated proposition is a universal affirmative (A), whose contradictory is the particular negative (O).

When an A proposition is false its contradictory O must be true, giving Statement 3.

Statement 2 (No students are serious) is the contrary (E), which stays undetermined and so is free to be true.

This follows from the contradictory relation of A and O together with the contrary relation of A and E on the square of opposition.