[AI 107A_B_4]

4. [15%] Consider the snapshot (shown to the right) of a (4x4) minesweeper game. Let A, B, C, D and E be propositional symbols representing whether mines exist at their locations. (a) [5%] Write down the propositional logic sentences according to the game rule, that is, a number at a location indicates the count of mines among its 8 neighboring locations. (b) [5%] Convert the sentences to conjunctive normal form. (c) [5%] Try to determine their truth values by repeatedly applying the resolution inference rule.

4. [15%] Consider the snapshot (shown to the right) of a (4x4) minesweeper game. Let A, B, C, D and E be propositional symbols representing whether mines exist at their locations. (a) [5%] Write down the propositional logic sentences according to the game rule, that is, a number at a location indicates the count of mines among its 8 neighboring locations. (b) [5%] Convert the sentences to conjunctive normal form. (c) [5%] Try to determine their truth values by repeatedly applying the resolution inference rule. 1 A B C 2 2 2 1 D 1 E 1 4. [15%] Consider the snapshot (shown to the right) of a (4x4) minesweeper game. Let A, B, C, D and E be propositional symbols representing whether mines exist at their locations. (a) [5%] Write down the propositional logic sentences according to the game rule, that is, a number at a location indicates the count of mines among its 8 neighboring locations. (b) [5%] Convert the sentences to conjunctive normal form. (c) [5%] Try to determine their truth values by repeatedly applying the resolution inference rule. 1 A B C 2 2 2 1 D 1 E 1