 Hi and welcome to the session. Let us understand the following question today. Determine whether the following relation is reflexive, symmetric and transitive. Given to us is relation r and the set Z of all integers defined as r is equal to x, y such that x minus y is an integer. Now let's proceed with the solution. Given to us is r is equal to x, y such that x minus y is an integer. It is a relation in the set of integers. Let's check for reflexivity. Now, x minus x is equal to 0 for all x belongs to Z and 0 is an integer. Therefore, r is reflexive. Let's check the symmetric property of the relation. Let x, y belongs to r, then x minus y is an integer. Now, minus of x minus y is also an integer. That is, y minus x is an integer. This implies y comma x belongs to r. Therefore, r is symmetric on Z. Let us see now for transitivity. Let x comma y belongs to r and y comma z belongs to r. Which implies x minus y is an integer. They are relation defined and y minus z is an integer. Similarly, by the relation defined. Now we know some of the two integers is also an integer. Therefore, x minus y plus y minus z is equal to x minus z is an integer. Therefore, x comma z belongs to r. And hence, r is transitive. Therefore, we can see that r is reflexive, r is symmetric and r is transitive. Therefore, the required answer is reflexive, symmetric and transitive. If you have understood the question, buy and have a nice day.