 Hello and welcome to the session. Let's discuss the following problem today. Show that the relation R in the set 1,2,3 given by R is equal to 1,2,1,2,1 is symmetric but neither reflects it nor transitive. Now let us write the solution. Let's set A is equal to 1,2,3 and R is equal to 1,2,2,1 is a relation defined in A. Now let us check for reflexivity. For 1 belongs to A, 1,1 does not belong to R, therefore R is not reflexive. Now let us check for symmetry. 1,2 belongs to R and 2,1 belongs to R, therefore R is symmetric. Now let us check for transitivity. We have 1,2 belongs to R and 2,1 belongs to R but 1,1 does not belong to R, therefore R is not transitive. Hence we approve R is symmetric and R is not reflexive and R is not transitive. I hope you understood this problem. Bye and have a nice day.