Realization of binary relation of discrete mathematics with C language and its properties

One 、 The experiment purpose Master the representation of binary relationship on computer , And it can be realized by computer to determine the nature of the relationship .

Two 、 Experimental content Program to judge whether a binary relationship is equivalent , If it is , Find its quotient set .（ You can use C or Python To write ）. Equivalence relation ： aggregate A The binary relationship on R At the same time, it is reflexive 、 Symmetry and transitivity , said R yes A The equivalence relationship on .

3、 ... and 、 Program design flow chart （ Or experimental principles ）   Result chart ： Code ： #include <stdio.h> #define MaxSize 10 char a[MaxSize][MaxSize]; int i, j, n; // Initialization matrix void Init() { printf(" Enter the total number of fields of binary relationship ：\n"); scanf("%d", &n); printf(" Please enter the relationship matrix .\n"); for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { scanf("%d", &a[i][j]); } } } // reflexivity int Reflexivity() { // The diagonal element is 0： That is, not satisfied for (int i = 0; i < n; ++i) { if (a[i][i] == 1) { printf("1. Have reflexivity \n"); return 1; } else if (a[i][i] != 1) { printf("1. Not reflexive \n"); return 0; } } return 1; } // symmetry int Symmetry() { for (int i = 0; i < n; ++i) { for (int j = 1; j < n; ++j) { if (a[i][j] == a[j][i]) // Symmetrical elements are not equal ： That is, the symmetry is not satisfied { printf("2. Have symmetry \n"); return 1; } else if (a[i][j] != a[j][i]) { printf("2. Without symmetry \n"); return 0; } break; } } return 1; } // Transitivity int Transitivity() { for (int i = 0; i < n; ++i) { for (int j = 0; j < n; ++j) { for (int k = 0; k < n; ++k) { if (a[i][j] && a[j][k] && !a[i][k]) { printf("3. It's not transitive \n"); return 0; } else { printf("3. Transitivity \n"); return 1; } } } } return 1; } // Quotient set void Quotient() { int c[MaxSize]; for (int i = 0; i < n; i++) c[i] = i + 1; // i On behalf of the i Elements printf("\n Quotient set is ：\n"); printf("{ "); for (int i = 0; i < n; i++) // Loop all elements { if (c[i]) { printf("{ "); for (int j = 0; j < n; j++) { if (a[i][j] && c[j]) { printf("%d ", c[j]); c[j] = 0; } } printf("} "); } } printf("}\n"); } int main() { Init(); // Initialization matrix if (Reflexivity() && Symmetry() && Transitivity()) { printf(" Therefore, there is an equivalence relationship \n"); // Print quotient set Quotient(); } else { printf(" Therefore, there is no equivalence relationship \n"); } }