Given the relation on 1 2 3 4 5 expressed by the following z

Given the relation on {1, 2, 3, 4, 5} expressed by the following zero-one matrix: [1 0 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 1 Is it reflexive? If not, what ordered pairs must be added to make it reflexive? Is it symmetric? If not, what ordered pairs must be added to make it symmetric? Is it antisymmetric? If not, what ordered pairs must be removed to make it antisymmetric? Is it transitive? If not, what ordered pairs must be added to make it transitive?

Solution

Answer:

A- No, (4,4) , For reflexive relation there should be a self loop in a graph and hence (1,1) (2,2) (3,3) (4,4) (5,5) should be 1
B- No (4,1) (5,2) (3,5) (5,4) (1,5) , For symmetricity in a relation the matriz should also be symmetric. If it isnt , make it.