FAeB T AeB FA TA FB T B Figure 1: Atomic tableau of e F(AeB)→(AV=B) T(AeB F(AV-B FA F-B T B T (AeB TA F B Figure 2: Tableau proof (a) The attack will succeed only if the enemy is taken by surprise or the position is weakly defended (b)The enemy will not be taken by surprise unless he is overconfident (c) The enemy will not be overconfident if the position is weakly defended (d)Therefore, the attack will not succeed Answer the following questions (7 marks (a) Translate the argument into propositions (4 marks) b) Use tableau proof to determine whether the argument is logically valid. 3 marks) Solution.(a)The proposition letters and its corresponding represented statement are as fo i. A: The attack will succeed B: The enemy is taken by surprise iii. C: The position is weakly defended iv. D: He is overconfident Then the statements can be represented as following: (each 0.5 mark) i.A→(BVC)F A ⊖ B F A T B T A ⊖ B T A F B Figure 1: Atomic tableau of ⊖ F (A ⊖ B) → (A ∨ ¬B) T (A ⊖ B) F (A ∨ ¬B) F A F ¬B T B T (A ⊖ B) T A F B ⊗ ⊗ Figure 2: Tableau proof (a) The attack will succeed only if the enemy is taken by surprise or the position is weakly defended. (b) The enemy will not be taken by surprise unless he is overconfident. (c) The enemy will not be overconfident if the position is weakly defended. (d) Therefore, the attack will not succeed. Answer the following questions: (7 marks) (a) Translate the argument into propositions. (4 marks) (b) Use tableau proof to determine whether the argument is logically valid. (3 marks) Solution. (a) The proposition letters and its corresponding represented statement are as following:(each 0.5 mark) i. A: The attack will succeed. ii. B: The enemy is taken by surprise. iii. C: The position is weakly defended. iv. D: He is overconfident. Then the statements can be represented as following:(each 0.5 mark) i. A → (B ∨ C). 2