 Hello and welcome to the session. Let us discuss the following problem today. Show that the relation r in the set r of the real numbers defined as r is equal to a,b such that a is less than equal to b square is neither reflexive nor symmetric nor transitive. Let us write the solution. Now r is equal to a,b such that a is less than equal to b square where a,b belongs to r. Now let us check for reflexivity. We see that 1 by 9 is less than equal to 1 by 9 the whole square which is not true. Therefore, it is not reflexive. Now let us check for symmetry. Let us consider plus 1 and less than equal to 1 square but 1 is not less than equal to half square that is a,b belongs to r but 1, half does not belong to r therefore r is not symmetric. Now let us check for transitivity. Now let us consider 2,-3 and minus 3,1. Now 2 is less than equal to minus 3 the whole square is true, minus 3 is less than equal to plus 1 the whole square is also true, less than equal to 1 square is not true. Therefore, for 2,-3 belongs to r and minus 3, plus 1 belongs to r we have 2,1 does not belong to r hence r is not transitive. We have proved r is not reflexive, r is not symmetric and r is not transitive. I hope you understood this problem. Bye and have a nice day.