When jesse first met nicolette, he extended his hand and said warmly, "nice to meet you." in response, nicolette sighed, rolled her eyes, and simply said, "yah," in a very sarcastic tone. jesse inferred that nicolette was not excited about meeting him based on her reaction. which rule of language did jesse likely base his decision on?

The correct answer is the pragmatic rule.
The pragmatic rule is the only one among these that incorporates non-verbal messages into the understanding as well - phonological, syntactic, and semantic rules have to rely only on words, which are not enough in real speech. Jesse didn't only base his conclusion on Nicolette's words, but also her sighing and rolling her eyes, which is something that only pragmatics can interpret.