Answer to Question #178253 in Discrete Mathematics for Ayesha

Question

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?

Answer 1

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