symbolize and proofs

Part 1. Symbolize the following sentences using propositional logic (2 pts each)


  1. Marvin drank the POISON and MARVIN is ill.
  2. If the diagnosis is CORRECT, then the INSURANCE company allowed the claim.
  3. The diagnosis is CORRECT.
  4. Provided that the diagnosis is CORRECT, JUAN will get the medicine if the DOCTOR will prescribe the medicine.
  5. Marvin drank the POISON only if MARVIN is ill.
  6. The INSURANCE company allowing the claim is a sufficient condition for JUAN getting the medicine. 7. LEWIS will confess or WILSON will get the death penalty, but not both.
  7. Neither did Johnson pull the TRIGGER nor is JOHNSON guilty.
  8. It is not the case that both LEWIS will confess and WILSON will get the death penalty.
  9. WILSON will get the death penalty if and only if LEWIS does not confess.



  1. Construct proofs for the following sequents. Even if you do not feel that you can get to the conclusion, try to do as many lines as you can since you will be given some points for attempting to do the proof. Each one is worth 10 points.


  1. R & (R→S), P & (P→T)├ S & T
  2. (A → B) & (A → C) ├ A→ (B & C)
  3. D → T, (D & T) → F ├ D → F
  4. A & B, (A → C) & (B→D) ├ C & D
  5. (P & R) → S, S ↔ T, ─T ├ R → ─P
  6. P v Q, P → (T → S), P → T, S ↔ Q ├ S
  7. A→(B→C), B & −C ├ −A
  8. R & S, S → (P → Q), Q → P ├ P ↔ Q


Ch. 9


  1. FvR, F→S, ─S, R→B ├ B (hint: use MT and DA in this proof)


5e. U→I, M→U ├ ─ I→ ─ M (hint: use arrow-in to get your conclusion; use MT in the process)


  1. O→(AvC), ─ A ├ O→C (hint: try using arrow-in to get your conclusion; use DA in the process)


  1. (C→S) & (─ C→S)├ S (hint: try using dash-out to get your conclusion; also use MT in the process)


10d. F→(L&A), ─ Lv ─ A├ ─F (hint: try using DM and MT)