Question

The question below consists of a main statement followed by four numbered statements. From the numbered statements, select the one that logically follows the main statement.
If the faculty is in the class, then the students will either study or keep quiet.

Options

• The students will not study or will not keep quiet, implies that the faculty is not in the class.

• If the faculty is not in the class, then the students will not study and will not keep quiet.

• The students will not study and will not keep quiet, implies that the faculty is not in the class.

• If the faculty is not in the class, then the students will not keep quiet or will not study.

Answer 1

P - If the faculty is in the class
q - then the students will either study 
Or r - keep quiet.

Statement: If p, then q or r.
Conclusions:
(i) p => q or r
(ii) ~q & ~r => ~p
(iii) p & -q => r
(iv) p & ~r => q

Conclusions:
(i) If the faculty is in the class, then either the students will study or they will keep quiet, (ii) The students are not studying and they are not keeping quiet, implies that the faculty is not in the class.
(iii) The faculty is in the class and the students are not studying, implies that they are keeping quiet.
(iv) The faculty is in the class and the students are not quiet, implies that they are studying.
Among the conclusions, (ii) is available as the third choice.