 Hello and welcome to the session, let us discuss the following problem today. Check whether the relation R in R defined by R is equal to A V star that A is less than equal to B Q is reflexive symmetric or transitive. Now let us write the solution. Now let us check for reflexivity. We have minus 2 comma minus 2 does not belongs to R as minus 2 is less than equal to minus 2 the whole cube which is not true therefore R is not reflexive. Now let us check for symmetry for elements 1 and 2 belongs to R we have 1 is less than equal to 2 cube but 2 is not less than equal to 1 cube therefore 1 comma 2 belongs to R but 2 comma 1 does not belongs to R therefore R is not symmetric. Now let us check for transitivity. Let us consider 2 comma cube root of 2 belongs to R and cube root of 2 comma 1.2 belongs to R. Therefore we have 2 is less than equal to cube root of 2 the whole cube which is true and for cube root of 2 comma 1.2 we have cube root of 2 is less than equal to 1.2 the whole cube which is again true because cube root of 2 is equal to 1.26 and 1.2 the whole cube is equal to 1.728 but 2 is not equal to 1.2 the whole cube that is 2 comma 1.2 does not belongs to R thus R is not transitive. So we have proved that R is not reflexive, R is not symmetric and finally R is not transitive. I hope you understood the session. Bye and have a nice day.