constructing proofs of their conclusions from their premises using the rules of inference we have studied in this course (included in the appendix). (5/30) (a)

constructing proofs of their conclusions from their premises using the rules of inference we have studied in this course (included in the appendix). (5/30) (a) 1.  P → Q 2. PvR 3. S 4. S → ~ Q       / R 5. ~Q  MT, 1 6. ~P   MT 1,5 7. ~ ~S.  DN 3,5 8. R.    DS 2,6 (b) 1. ~A → [A v (B →C)] 2. (B v D) → ~A 3. B v D 4. C → A         / D 5. (c)    1. P → (Q v R) 2. ~ Q . R       / R (d) 1. (~A v B) → (G → D) 2. (G v E) → (~A → F) 3. A v G 4. ~A           / F . D (e) 1. A → (C v B) 2. ~C . A 3. B → D        / D IV. Symbolize the following arguments, then show that they are valid by constructing proofs of their conclusions from their premises. (4/30) a) If Peters went to the lecture, then Russel did too. But if Quine went, Sellers did too. Either Peters or Quine went, But Sellars didn’t. So, Russell went. (P, R, Q, S) b) If killing is always wrong, then war is always wrong. If war is always wrong, then we should have allowed tler to rule the world. We should not have allowed tler to rule the world. Killing is not always wrong. (K, W, H) V. Draw a Venn diagram for each of the following categorical statement. (2/30) (a) Not all lawyers are rich. (b) There is something and it is a horse. (c) Only reptiles are snakes. VI. Draw a Venn diagram for each of the following categorical syllogisms, and then circle whether it is valid or invalid (8/30). (a) All flying squirrels are mammals. No birds are mammals. Therefore, no flying squirrels are birds. Valid         Invalid (b) No Martians speak English. All officers on the Starship do not speak English. Therefore, all officers on the Starship are Martians. Valid        Invalid (c) Some parrots are not pests. All parrots are pets. So, no pets are pests. Valid         Invalid (d) All doctors are educated. Some doctors are clowns. So, some clowns are educated. Valid    Invalid