Either roman has a date with malou, or jeff is sleeping or hadji is eating.

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.

Either Roman has a date with Malou, or Jeff is sleeping or Hadji is eating. - True b. Either Jeff is sleeping or Hadji is not eating - True c. Roman and Malou are on a date and Jeff is sleeping, or Hadji is not eating. - False