Given that one Friday night, Roman and Malou are busy studying for their Logic exam. Meanwhile, Hadji just tweeted a picture of himself eating crispy pata and sisig. Jeff is sound asleep in his dorm room.
Part A:
The truth value of "Either Roman has a date with Malou, or Jeff is sleeping or Hadji is eating." is obtained as follows:
From the scenario, the truth value of the individual statements are as follows:
Roman has a date with Malou is True
Jeff is sleeping is True
Hadji is eating is True
Thus, the truth value of "True" or "True" or "True" is True.
Therefore, the truth value of "Either Roman has a date with Malou, or Jeff is sleeping or Hadji is eating." is True.
Part B:
The truth value of "Either Jeff is sleeping or Hadji is not eating" is obtained as follows:
From the scenario, the truth value of the individual statements are as follows:
Jeff is sleeping is True
Hadji is not eating is False
Thus, the truth value of "True" or "False" is True.
Therefore, the truth value of "Either Jeff is sleeping or Hadji is not eating" is True.
Part C:
The truth value of "Roman and Malou are on a date and Jeff is sleeping, or Hadji is not eating." is obtained as follows:
From the scenario, the truth value of the individual statements are as follows:
Roman and Malou are on a date is True
Jeff is sleeping is True
Hadji is not eating is False
The truth value of "True" and "True" is True.
The truth value of "True" or "False" is True.
Thus, the truth value of ("True" and "True") or "False" is True.
Therefore, the truth value of "Roman and Malou are on a date and Jeff is sleeping, or Hadji is not eating." is True.