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离散数学笔记 1.2:命题逻辑的应用

\4. To use the wireless network in the airport you must pay the daily fee unless you are a subscriber to the service. Express your answer interms of w:“You can use the wireless network in the airport,” d: “You pay the daily fee,” and s: “You are a subscriber to the service.”

$d\or s \to w$

\18. When planning a party you want to know whom to invite. Among the people you would like to invite are three touchy friends. You know that if Jasmine attends, she will become unhappy if Samir is there, Samir will attend only if Kanti will be there, and Kanti will not attend unless Jasmine also does. Which combinations of these three friends can you invite so as not to make someone unhappy?

假定 $P_X$ 表示 $X $ will attend。

  • if Jasmine attends, she will become unhappy if Samir is there $P_J \to \neg P_S$
  • Samir will attend only if Kanti will be there, and $P_K \to P_S$
  • Kanti will not attend unless Jasmine also does. $P_J \to P_K$

    也即:

    $$
    P_{S} \Rightarrow P_{K} \Rightarrow P_{J} \Rightarrow \neg P_{S}
    $$

    我们的目标是最少的 $\neg$ 最优解是不邀请任何人。

\40. Find the output of each of these combinatorial circuits.

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做这道题我们学习一些简单的逻辑门

image-20200407120011412

  1. 非门
  2. 或门
  3. 与门

a) $\neg p \or \neg q$

b) $\neg()(\neg p \and q)\or p)$

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