 Hello and welcome to the session, let us consider the following problem today. Determine whether the following relation is reflexive, symmetric and transitive. Given to us the relation r in the set A of human beings in a town at a particular time given by, first r is equal to x, y such that x and y work at the same place. Second, r is equal to x and y such that x and y live in the same locality. Third, r is equal to x, y such that x is exactly 7 centimeter taller than y. Fourth, r is equal to x, y such that x is a y for y. And last one is r is equal to x, y such that x is the father of y. Now let us write the solution. Here we are discussing all the parts separately. Given to us is set A is equal to human beings at a particular time. This is called the first part. I said that x and y at same place take for reflexivity. It belongs to r, therefore let us check for symmetry. It belongs to r, x belongs to r, therefore r is symmetric. Now let us check for transitivity. Now y belongs to r, belongs to r, then x, z belongs to r. Since y, z at same place, therefore r is transitive. This is the next part. r is equal to x, y such that x and y live in the same locality. Let us check for reflexes to r, therefore it is reflexive. Let us check for symmetric. Somehow y belongs to r, belongs to r, check for transitivity. Longs to r belongs to r, z belongs to r, since same locality is called the next part. Given to us is r is equal to x, y such that x is exactly 7 centimeter taller than y. Now let us check for reflexivity. It cannot be 7 centimeter, belongs to r, not reflexive. Let us check for symmetry. Longs to r, then 7 centimeter taller than y, which implies cannot be 7 centimeter taller than x, which implies y, x does not belong to r, not symmetric. Now let us check for transitivity, belongs to r, which implies x is exactly meter taller than y, 7 centimeter taller than z, which implies cannot be exactly 7 centimeter taller than z, comma z does not belong to r, not symmetric. Let us study next part. Given to us r is equal to x, y such that x is a y for y. Now let us check for reflexive. Somehow y belongs to r, cannot be y for x. Let us check for symmetry. Longs to r, which means x is a y for y, it is not possible. Now let us check for transitivity. Somehow y belongs to r, we cannot find belongs to r. Let us do the last part. Given to us r is equal to x, y such that x is a father of y. Let us check for reflexivity. It says, let us check for symmetry. Somehow y belongs to r, which implies x is a father of y, which implies y cannot be father of x, which implies y comma x does not belong to r, which implies r is not symmetric. Let us check for transitivity. x comma y belongs to r and z belongs to r. It implies x is a father of y, the father of z, that does not belong to r. I hope you understood this problem. Bye and have a nice day.