Here you go!
a := ang lives with the emperor
b := bao loves the emperor
c := chang loves the emperor
d := di loves the emperor
e := eng loves the emperor
Want to show that
We know that e = F. Then . But , so
we know that . Therefore, either b=F or d=F.
Next, we know that either ~c or a^d is true. We also know that ~a or b is true.
Case 1. Suppose b=F. Then ~a has to be true, and so a is false. Then (a^d) is false, so ~c is true, and so c is false.
Case 2. Suppose d=F. Then ~c has to be true, and so c is false.
Since c is false in both cases, Chang does not love the emperor.