An internal conflict; the protagonist vs. internalized social forces.
The internal conflict can also develop between the protagonist and herself. However, this is not the case here, as she is struggling to overcome the supposed obstacles that others (her family) are imposing upon her. It's not that she doubts her own capabilities or competence; it's that others doubt her capabilities, based on the fact that she is a woman.
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The type of novel that deals with the customs of a particular social class is the B. novel of manners.
Here are some examples of novels of manners:
- Sense and Sensibility, Pride and Prejudice, Emma, Persuasion, written by Jane Austen
That means to be in a bad situation, or to just get in trouble.