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 it is a Thursday, then I will go to the cinema or I will sleep.
It is not a Thursday, implies that I am not going to cinema and I am not sleeping.
It is a Thursday and I am not sleeping means that I am going to cinema.
I am not going to cinema and I am sleeping, means that it is a Thursday.
None of these
p - If It is a Thursday,
q - then I will go to cinema
or r - I will sleep.
The implications of the above statements are
(i) p and ~q => r
(ii) p and ~r => q
(iii) ~q and ~ r => ~p.
Choice (2) is implication (ii).
So, "It is a Thursday and I am not sleeping means that I am going to the cinema." is the correct option.