A 39-year-old man is brought to the emergency department because of abdominal pain in the area under his groin. The pain began suddenly while he was helping a coworker lift a scaffold. He had an unremarkable appendectomy 3 months ago. Physical examination shows a bulge in the area, worse with coughing, grunting, and squatting. The bulge is easily reducible in the right groin area. The patient denies nausea, vomiting, diaphoresis, and diarrhea. Radiograph and laboratory studies are negative for strangulation. Which of the following nerves was most likely damaged during the appendectomy procedure?