Question

8. Write the argument in symbolic form using the indicated letters and construct a formal proof of the validity of the argument. (a) If Emery studies (S), Emery will graduate (G). If Emery graduates, Emery will travel (T) or Emery will work for his uncle (U). Emery studies, but Emery does not work for his uncle. Therefore, Emery will travel. (b) If Robin goes to the state park (P), Robin hikes (H) and Robin fishes (F). Robin did not hike or Robin did not fish or Robin did camp (C). Robin did not camp. Therefore, Robin did not go to the state park.

Answer 1

a) S rightarrow G G rightarrow T or U S similarto U T 1. S rightarrow G 2. S }given 3. G MP, 1, 2 4. G rightarrow T or U given 5. T or U MP, 3, 4 6. Similarto U rightarrow T (Definition of v) 7. Similarto U given 8. T MP, 6, 7 b) P rightarrow H and F similarto H or similarto F or C similarto C similarto P 1. Similarto H or similarto F or C given 2. Similarto C given 3. Similarto H or similarto F (By definition of V) 4. similarto(H and F) (De-Morgan) 5. P rightarrow H and F given 6. similarto(A and F) rightarrow similarto P (Ax 2 of propositional Logic) 7. similarto P (Mp 4, 6)