离散数学实验报告-利用真值表法求主析取范式以及主合取范式（内含源码和实验报告）.zip

//(P∧Q) V (┓P∧R) //主合取范式: (┓PVQV┓R) ∧ (┓PVQVR) ∧ (PV┓QVR) ∧ (PVQVR) //主析取范式: (P∧Q∧R) V (P∧Q∧┓R) V (┓P∧Q∧R) V (┓P∧┓Q∧R) #include <iostream> #include <cmath> using namespace std; int a[1000], b[1000], c[1000]; //P∧Q ┓P∧R A int x[1000], y[1000], z[1000]; //P Q R int n; //输出真值表 void Output_truth_table() { cout << endl << "真值表:" << endl; cout << 'P' << '\t' << 'Q' << '\t' << 'R' << '\t'; cout << "P∧Q" << '\t' << "┓P∧R" << '\t' << "(P∧Q) V (┓P∧R)" << endl; for (int i = 0; i < pow(2, n); ++i) { //输出 P Q R 的真值 if (i < pow(2, n - 1)) { x[i] = 1; cout << 'T' << '\t'; } if (i >= pow(2, n - 1)) { x[i] = 0; cout << 'F' << '\t'; } if (i % 4 < 2) { y[i] = 1; cout << 'T' << '\t'; } if (i % 4 >= 2) { y[i] = 0; cout << 'F' << '\t'; } if (i % 2 == 0) { z[i] = 1; cout << 'T' << '\t'; } if (i % 2 == 1) { z[i] = 0; cout << 'F' << '\t'; } //输出(P∧Q) (┓P∧R) (P∧Q) V (┓P∧R) 的真值 if (a[i] == 1) cout << 'T' << '\t'; else if (a[i] == 0) cout << 'F' << '\t'; if (b[i] == 1) cout << 'T' << '\t'; else if (b[i] == 0) cout << 'F' << '\t'; if (c[i] == 1) cout << 'T' << endl; else if (c[i] == 0) cout << 'F' << endl; } } //主合取范式 void Master_conjunction() { cout << endl << "主合取范式: "; int count = 0; for (int i = 0; i < pow(2, n); ++i) { if (c[i] == 0) { //如果公式真值为假，则输出相应的真值相反的 P Q R if (x[i] == 1 && y[i] == 1 && z[i] == 1) { cout << "(┓PV┓QV┓R)"; count++; } else if (x[i] == 1 && y[i] == 1 && z[i] == 0) { cout << "(┓PV┓QVR)"; count++; } else if (x[i] == 1 && y[i] == 0 && z[i] == 1) { cout << "(┓PVQV┓R)"; count++; } else if (x[i] == 1 && y[i] == 0 && z[i] == 0) { cout << "(┓PVQVR)"; count++; } else if (x[i] == 0 && y[i] == 1 && z[i] == 1) { cout << "(PV┓QV┓R)"; count++; } else if (x[i] == 0 && y[i] == 1 && z[i] == 0) { cout << "(PV┓QVR)"; count++; } else if (x[i] == 0 && y[i] == 0 && z[i] == 1) { cout << "(PVQV┓R)"; count++; } else if (x[i] == 0 && y[i] == 0 && z[i] == 0) { cout << "(PVQVR)"; count++; } if (count != pow(2, n - 1)) cout << " ∧ "; } } cout << endl; } //主析取范式 void Master_disjunction() { cout << endl << "主析取范式: "; int count = 0; for (int i = 0; i < pow(2, n); ++i) { if (c[i] == 1) { //如果公式真值为真，则输出相应真值的 P Q R if (x[i] == 1 && y[i] == 1 && z[i] == 1) { cout << "(P∧Q∧R)"; count++; } else if (x[i] == 1 && y[i] == 1 && z[i] == 0) { cout << "(P∧Q∧┓R)"; count++; } else if (x[i] == 1 && y[i] == 0 && z[i] == 1) { cout << "(P∧┓Q∧R)"; count++; } else if (x[i] == 1 && y[i] == 0 && z[i] == 0) { cout << "(P∧┓Q∧┓R)"; count++; } else if (x[i] == 0 && y[i] == 1 && z[i] == 1) { cout << "(┓P∧Q∧R)"; count++; } else if (x[i] == 0 && y[i] == 1 && z[i] == 0) { cout << "(┓P∧Q∧┓R)"; count++; } else if (x[i] == 0 && y[i] == 0 && z[i] == 1) { cout << "(┓P∧┓Q∧R)"; count++; } else if (x[i] == 0 && y[i] == 0 && z[i] == 0) { cout << "(┓P∧┓Q∧┓R)"; count++; } if (count != pow(2, n - 1)) cout << " V "; } } cout << endl; } int main() { cout << "请输入变量:"; cin >> n; cout << endl << "公式为:(P∧Q) V (┓P∧R)" << endl; int m1 = 0; int m2 = 0; int m3 = 0; //三重循环 for (int i = 0; i < 2; ++i) { for (int j = 0; j < 2; ++j) { for (int k = 0; k < 2; ++k) { if (i == 0 && j == 0) { a[m1++] = 1; //P为真，Q为真：P∧Q 为真 } if (j == 1 || i == 1) { a[m1++] = 0; //P为真，Q为假 或 P为假：P∧Q 为假 } if (i == 0 || k == 1) { b[m2++] = 0; //P为真 或 P为假，R为假：(┓P∧R)为假 } if (i == 1 && k == 0) { b[m2++] = 1; //P为假 且 R为真：(┓P∧R)为真 } } } } for (int m3 = 0; m3 < pow(2, n); ++m3) { if (a[m3] == 0 && b[m3] == 0) { //P∧Q 为假 且 (┓P∧R)为假 c[m3] = 0; } else c[m3] = 1; } Output_truth_table(); Master_conjunction(); Master_disjunction(); return 0; }