The writers for a TV show have determined that they need to add a new character. One demographic wants the new character to be a man, or someone who can do martial arts. Another demographic wants the new character to be a woman, or someone who is a medical doctor. The writers want to please both demographics. Therefore, the new character will be someone who can do martial arts or is a medical doctor.
Which rule of inference was used here?
A. Conjunction
B. Resolution
C. Modus Ponens
D. Disjunctive Syllogism
E. Hypothetical Syllogism
F. Addition
G. Modus Tollens
H. Simplification

The rule of inference that was used here is Resolution. We should note that the resolution principle is used to know whether an argument is valid or not and hence make conclusion.

Resolution typically complements the sentences given such that the new clause has every information given and satisfies everyone.

We can see that from the question, one demographic wants the new character to be a man, or someone who can do martial arts while the other demographic wants a woman,or a medical doctor. Eventually, the writers want to please both demographics and said that the new character will be a martial artsmist or a medical doctor.