离散数学,基础公式模板
离散数学,基础公式模板

联结词真值表和编程中的位运算符对应
联结词真值表和编程中的位运算符对应

等值演算公式 和 集合恒等式公式 一样

常见符号

合取 ∧∧∧∧∧∧
∧∧∧∧∧∧
非 ┐┐┐;-┐┐
⇔⇔⇔⇔ ⇔⇔⇔⇔⇔⇔⇔
蕴含 →→→→→→ →→→→
全称量词 ∀∀∀∀∀∀
存在量词 ∃∃∃∃∃

∀：全称量词∀xP(x)表示P(x)的全称量化 后面是蕴含符号
∃：存在量词 后面是合取符号

p->q 只有q才p
p->q 只有q才p

联结词真值表

联结词真值表

联结词真值表

真值表

3个变元的真值表

p q r
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

4个变元的真值表

p q r s
0 0 0 0
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 0
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1

数据库写真值表

3个变元的真值表

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CREATE TABLE `bei_math_301_copy1`  (
  `id` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL,
  `fields_1` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL,
  `fields_2` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL,
  `fields_3` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL,
  `compute_1` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL,
  `compute_2` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL,
  `compute_3` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL,
  `compute_4` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL,
  `other_sql` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL
) ENGINE = MyISAM CHARACTER SET = utf8mb4 COLLATE = utf8mb4_general_ci ROW_FORMAT = Dynamic;


INSERT INTO `bei_math_301_copy1` VALUES ('序号', 'p', 'q', 'r', NULL, NULL, NULL, NULL, 'SELECT fields_1,fields_2,fields_3 FROM bei_math_301 GROUP BY fields_1,fields_2,fields_3;');
INSERT INTO `bei_math_301_copy1` VALUES ('1', '0', '0', '0', NULL, NULL, NULL, NULL, '这是校验是否有写错的值');
INSERT INTO `bei_math_301_copy1` VALUES ('2', '0', '0', '1', NULL, NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_301_copy1` VALUES ('3', '0', '1', '0', NULL, NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_301_copy1` VALUES ('4', '0', '1', '1', NULL, NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_301_copy1` VALUES ('5', '1', '0', '0', NULL, NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_301_copy1` VALUES ('6', '1', '0', '1', NULL, NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_301_copy1` VALUES ('7', '1', '1', '0', NULL, NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_301_copy1` VALUES ('8', '1', '1', '1', NULL, NULL, NULL, NULL, NULL);

4个变元的真值表

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CREATE TABLE `bei_math_401_copy1`  (
  `id` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL,
  `fields_1` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL,
  `fields_2` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL,
  `fields_3` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL,
  `fields_4` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL,
  `compute_1` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL,
  `compute_2` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL,
  `compute_3` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL,
  `other_sql` varchar(255) CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci NULL DEFAULT NULL
) ENGINE = MyISAM CHARACTER SET = utf8mb4 COLLATE = utf8mb4_general_ci ROW_FORMAT = Dynamic;



INSERT INTO `bei_math_401_copy1` VALUES ('序号', 'p', 'q', 'r', 's', NULL, NULL, NULL, 'SELECT fields_1,fields_2,fields_3,fields_4 FROM bei_math_401 GROUP BY fields_1,fields_2,fields_3,fields_4;');
INSERT INTO `bei_math_401_copy1` VALUES ('1', '0', '0', '0', '0', NULL, NULL, NULL, '这是校验是否有写错的值-fei');
INSERT INTO `bei_math_401_copy1` VALUES ('2', '0', '0', '0', '1', NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_401_copy1` VALUES ('3', '0', '0', '1', '0', NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_401_copy1` VALUES ('4', '0', '0', '1', '1', NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_401_copy1` VALUES ('5', '0', '1', '0', '0', NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_401_copy1` VALUES ('6', '0', '1', '0', '1', NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_401_copy1` VALUES ('7', '0', '1', '1', '0', NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_401_copy1` VALUES ('8', '0', '1', '1', '1', NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_401_copy1` VALUES ('9', '1', '0', '0', '0', NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_401_copy1` VALUES ('10', '1', '0', '0', '1', NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_401_copy1` VALUES ('11', '1', '0', '1', '0', NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_401_copy1` VALUES ('12', '1', '0', '1', '1', NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_401_copy1` VALUES ('13', '1', '1', '0', '0', NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_401_copy1` VALUES ('14', '1', '1', '0', '1', NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_401_copy1` VALUES ('15', '1', '1', '1', '0', NULL, NULL, NULL, NULL);
INSERT INTO `bei_math_401_copy1` VALUES ('16', '1', '1', '1', '1', NULL, NULL, NULL, NULL);

等值验算公式16条

等值演算公式 和 集合恒等式公式 一样

等值验算公式

等值验算公式

推理定理8条

假言推理和拒取式 口诀: 肯前肯后,否后否前

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假言推理，是在蕴含表达式中，肯定前件，得到后件成立的结论。
假言的意思，就是在蕴含表达式，假设前件成立，得到后件成立

拒取式，是在蕴含表达式中，否定后件，得出否定前件的结论。
说通俗一点，就是通过得知后件为假时，拒绝接受前件，所以叫拒取式

析取三段论 口诀: 卧龙凤雏得一可安天下,凤雏嗝屁剩卧龙

推理定理8条

一阶逻辑等值式

换名规则,代替规则

一阶逻辑等值式

一阶逻辑等值式推导

一阶逻辑推理定理4条

一阶逻辑推理定理

集合恒等式公式16条

等值演算公式 和 集合恒等式公式 一样

常识

文氏图

集合恒等式公式

底部

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