用法查询_离散数学_必背公式

一时失言乱红尘 2022-10-23 02:55 201阅读 0赞

# **基本等价公式** #

**设****G****，****H****，****S****是任何的公式，则：**

G∨(H∨S)＝(G∨H)∨S  (结合律)

G∧(H∧S)＝(G∧H)∧S

G∨H＝H∨G                (交换律)

G∧H＝H∧G

G∨G＝G                      (幂等律)

G∧G＝G

G∨(G∧H)＝ G              (吸收律：符号相反，内外都有，则吸收)

G∧(G∨H)＝ G

G∨(H∧S)＝(G∨H)∧(G∨S)  (分配律）

G∧(H∨S)＝(G∧H)∨(G∧S)

G∨0＝G  (同一律)

G∧１＝G

G∨１＝１  (零律)

G∧0＝0

G∨┐G ＝１  (排中律)

G∧┐G ＝0  (矛盾律)

┐(┐G)＝G  (双重否定律)

┐(G∨H)＝┐G∧┐H  (De MoRGan定律)

┐(G∧H)＝┐G∨┐H

(G![\\leftrightarrow][leftrightarrow]H)＝(G→H)∧(H→G)  (等价式)

(G→H)＝(┐G∨H)  (蕴涵式)

G →Ｈ＝┐Ｈ→┐G  (假言易位)

G ![\\leftrightarrow][leftrightarrow]Ｈ＝┐G![\\leftrightarrow][leftrightarrow]┐Ｈ  (等价否定等式)

(G →Ｈ) ∧(G→┐Ｈ)＝┐G  (归谬论)

# **推理定律** #

设A,B,C,D是任意的命题公式，则有：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FpcXExMzY_size_16_color_FFFFFF_t_70][]

# 谓词逻辑等值演算与推理 #

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FpcXExMzY_size_16_color_FFFFFF_t_70 1][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FpcXExMzY_size_16_color_FFFFFF_t_70 2][]

# 前束范式转化方法 #

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FpcXExMzY_size_16_color_FFFFFF_t_70 3][]

# 谓词逻辑推理公式 #

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2FpcXExMzY_size_16_color_FFFFFF_t_70 4][]

[leftrightarrow]: https://private.codecogs.com/gif.latex?%5Cleftrightarrow
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