離散數(shù)學浙大講義11邏輯-文庫吧資料
2025-10-01 16:50本頁面
【正文】 r from campus only if you are a puter science major or you are not a freshman, Solution: a → (c ∨ f ). ?Logic 命題邏輯 10/23/2022 3:27 PM Deren Chen, ZheJiang Univ. 30 EXAMPLE 9 How can the following English sentence be translated into a logical expression? You cannot ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old. Solution: (r∧ s) → q. ??Logic 命題邏輯 10/23/2022 3:27 PM Deren Chen, ZheJiang Univ. 31 EXAMPLE 10 說離散數(shù)學是枯燥無味的或毫無價值的，那是不對的。Today is not Friday. Logic 命題邏輯 10/23/2022 3:27 PM Deren Chen, ZheJiang Univ. 13 Table 1 Logic 命題邏輯 10/23/2022 3:27 PM Deren Chen, ZheJiang Univ. 14 DEFINITION 2. Let p and q be propositions. The proposition p and q, denoted by p∧ q, is the proposition that is true when both p and q are true and is false otherwise. The proposition p∧ q is called the conjunction of p and q. The truth table for p∧ q is shown in Table 2. p和 q的合取 Logic 命題邏輯 10/23/2022 3:27 PM Deren Chen, ZheJiang Univ. 15 Table 2 Logic 命題邏輯 10/23/2022 3:27 PM Deren Chen, ZheJiang Univ. 16 EXAMPLE 4 Find the conjunction of the propositions p and q where p is the proposition Today is Friday and q is the proposition It is raining today. Solution: The conjunction of these propositions, p∧ q, is the proposition Today is Friday and it is raining today. This proposition is true on rainy Fridays and is false on any day that is not a Friday and on Fridays when it does not rain. Logic 命題邏輯 10/23/2022 3:27 PM Deren Chen, ZheJiang Univ. 17 DEFINITION 3. Let p and q be proposition p or q, denoted by p∨ q, is the proposition that is false when p and q are both false and true otherwise. The proposition p∨ q is called the disjunction of p and q. The truth table for p∨ q is shown in Table 3. p和 q的析取 Logic 命題邏輯 10/23/2022 3:27 PM Deren Chen, ZheJiang Univ. 18 Table 3 Logic 命題邏輯 10/23/2022 3:27 PM Deren Chen, ZheJiang Univ. 19 EXAMPLE 5 What is the disjunction of the propositions p and q where p and q are the same propositions as in Example 4? Solution: The disjunction ofp and q, p∨ q, is the proposition Today is Friday or it is raining today.
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