 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 that relation R in the set A is equal to elements 1, 2, 3, 4, 5, 6 as R is equal to x, y sub that y is divisible by x. Now let us proceed with the solution. Given to us is R is equal to x, y sub that y is divisible by x. It is a relation in set A which is equal to 1, 2, 3, 4, 5, 6. Now let us check for reflexivity. x is divisible by x for all x belongs to A. Therefore x, x belongs to R for all x belongs to A. Therefore R is reflexive. Now let us see for symmetric. Let us consider 6 is divisible by 2 but 2 is not divisible by 6. Here 2, 6 belongs to R but 6, 2 does not belongs to R. Therefore R is not symmetric. Now let's check for transitivity. Let x, y belongs to R and y, z belongs to R which implies y is divisible by x and z is divisible by y. Therefore z is divisible by x. Therefore x, z belongs to R. Hence R is transitive. Therefore we can see that R is reflexive, R is not symmetric and R is transitive. Therefore the final answer is reflexive and transitive but not symmetric. I hope you enjoyed this session. Bye and have a nice day.