There are ___ satisfying assignments to (¬w∧x∧¬y∧¬z)∨(¬w∧¬x∧y)∨(¬w∧¬x∧z)(\neg w \wedge x \wedge \neg y \wedge \neg z) \vee (\neg w \wedge \neg x \wedge y) \vee (\neg w \wedge \neg x \wedge z)(¬w∧x∧¬y∧¬z)∨(¬w∧¬x∧y)∨(¬w∧¬x∧z).
參考答案與解析
共有 4 組滿足指派。以窮舉全部16組(w,x,y,z)(w,x,y,z)(w,x,y,z)真值指派驗證:(¬w∧x∧¬y∧¬z)∨(¬w∧¬x∧y)∨(¬w∧¬x∧z)(\neg w\wedge x\wedge\neg y\wedge\neg z)\vee(\neg w\wedge\neg x\wedge y)\vee(\neg w\wedge\neg x\wedge z)(¬w∧x∧¬y∧¬z)∨(¬w∧¬x∧y)∨(¬w∧¬x∧z)在w=0w=0w=0時的4種(x,y,z)(x,y,z)(x,y,z)組合成立:(1,0,0),(0,1,0),(0,1,1),(0,0,1)(1,0,0),(0,1,0),(0,1,1),(0,0,1)(1,0,0),(0,1,0),(0,1,1),(0,0,1),其餘(含所有w=1w=1w=1的情況)皆不成立。