Formalize the following argument, then determine the result using logical Inferences Either Derek works or Avery does not work. If it is not true that both Avery works and Brandon does not work, then clearly Celina does not work. However, Derek does not work." Does Celina work?

Let,

A: Avery Works

B: Brandon Works

C: Celina Works

D: Derek Works

1. $D\lor\neg A\\$
2. $\neg(A \land \neg B)\rightarrow \neg C$
3. $\neg D$
4. $\neg A$ Using 1,3, Disjunction Syllogism
5. $\neg A\lor B$ Using 4, vE
6. $\neg(A\land \neg B)$ Using 5, Demorgans
7. $\neg C$ Using 2,6, Modus Ponens

Conclusion: From point 7 it is clear that Celina doesn't work