Final answer:
The logical fallacy exhibited in the statement about kids having a party and subsequently never staying on top of their studies is an example of a slippery slope, which implies that an initial action will lead to an extreme outcome without sufficient evidence. Option a is the correct answer.
Step-by-step explanation:
The statement "You can't let your kids have a party this weekend. If you do that, they'll want to do it every single weekend, and they'll never stay on top of their studies." presents a type of logical fallacy. In this case, the fallacy used is a slippery slope.
A slippery slope fallacy occurs when an argument suggests that a relatively small first step leads to a chain of related events culminating in some significant (usually negative) effect, without providing sufficient evidence that this chain of events will occur.
The speaker's assertion moves from a single occurrence (allowing a party for one weekend) to an extreme, unfounded outcome (never staying on top of their studies), without any logical connection between the events beyond speculation.