Question

For a possible 9 points of extra credit, complete the following proof. Derive the required conclusion using the given assumptions and some combination of the 18 rules of inference. You can copy and paste the symbols from the given lines if you don't know how to bring them up in the editor. 1. [A∨(B−C)]≡D 2. ∼D/B∼C

Answer 1

To derive the required conclusion using the given assumptions and rules of inference, you can use the disjunctive syllogism and modus tollens rules.

Step-by-step explanation:

To derive the required conclusion, we can use the rules of inference. Given the first assumption and the equivalence, we can use the disjunctive syllogism rule. Here are the steps:

1. From assumption 1, we have [A∨(B−C)]≡D.
2. Using the disjunctive syllogism rule, we can derive D from [A∨(B−C)].
3. From assumption 2, we have ∼D/B∼C.
4. Using modus tollens, we can derive ∼C from ∼D.

Therefore, the required conclusion is ∼C (not C).