2. (Single Agent Modal Logic) (Total: 25 marks) (a) Determine whether Oxp+q) (OpA 00-0) is valid. If it is valid, explain why it is valid If it is not valid, provide a counterexample and show that it is a counterexample (7 marks) (b) Let M - (W.AV) be given by W - W. W. Ws, w.)R. (ww.). (ww.). (ww.). (wy, ws)), V(p) - {W, wy). Draw this model. (3 marks) (c) For the model described in (b), explain whether MW-0001 (4 marks) (d) Give a proof in the proof system K of Oppva)). (11 marks) 2. (Single Agent Modal Logic) (Total: 25 marks) (a) Determine whether Oxp+q) (OpA 00-0) is valid. If it is valid, explain why it is valid If it is not valid, provide a counterexample and show that it is a counterexample (7 marks) (b) Let M - (W.AV) be given by W - W. W. Ws, w.)R. (ww.). (ww.). (ww.). (wy, ws)), V(p) - {W, wy). Draw this model. (3 marks) (c) For the model described in (b), explain whether MW-0001 (4 marks) (d) Give a proof in the proof system K of Oppva)). (11 marks)