After-school activities running late entails that the buses will run late. The buses running late is a sufficient condition for either Carlos and Deandra getting home late or Edna missing dinner. Either after-school activities run late but Carlos doesn't get home late, or after-school activities run late but Deandra doesn't get home late. So, Edna misses dinner.
-Which of the following is the best translation into PL of this argument?
A) A ⊃ B B ⊃ [(C • D) $ \lor $ E]
(A $ \lor $ ∼C) $ \lor $ (A $ \lor $ ∼D) / E
B) A ⊃ B B ⊃ [(C • D) $ \lor $ E]
(A • ∼C) $ \lor $ (A • ∼D) / E
C) A ⊃ B [(C • D) $ \lor $ E] ⊃ B
(A • ∼C) $ \lor $ (A • ∼D) / E
D) A ⊃ B [(C • D) $ \lor $ E] ⊃ B
(A $ \lor $ ∼C) $ \lor $ (A $ \lor $ ∼D) / E
E) A ⊃ B [(C • D) $ \lor $ E] ⊃ B
(A $ \lor $ ∼C) • (A $ \lor $ ∼D) / E

Question

Quizplus · Accepted Answer

Option B correctly translates the argument into propositional logic (PL). It captures the structure of the argument by stating that after-school activities running late (A) is a sufficient condition for the buses running late (B), which in turn is a sufficient condition for either both Carlos and Deandra getting home late (C • D) or Edna missing dinner (E). The premises that either after-school activities run late but Carlos doesn't get home late, or after-school activities run late but Deandra doesn't get home late, are correctly represented as a disjunction of conjunctions (A • ∼C) $ \lor $ (A • ∼D), leading to the conclusion that Edna misses dinner (E).

After-School Activities Running Late Entails That the Buses Will Run ∨ \lor ∨

After-School Activities Running Late Entails That the Buses Will Run $\lor$