 Hello and welcome to the session. Let us understand the following question today. Determine whether the following relation is reflexive, symmetric and transitive. Relation r and the set n of natural numbers defined as r is equal to x, y such that y is equal to x plus 5 and x is less than 4. Now before writing the solution let us define the relation. The relation r in a set a is called reflexive if a, a belongs to r for every a belongs to a. Symmetric if a1, a2 belongs to r which implies a2, a1 belongs to r. For all a1, a2 belongs to a and transitive if a1, a2 belongs to r and a2, a3 belongs to r which implies a1, a3 belongs to r. For all a1, a2, a3 belongs to a. Now this is the key idea towards our question. Now let us proceed with the solution. It is given to us that r is equal to x, y such that y is equal to x plus 5 and x is less than 4. It is a relation in a set of n that is natural numbers. So now let us find the elements of r. Therefore r is equal to, for x is equal to 1, y is equal to 6, so 1, 6. For x is equal to 2, y is equal to 7 and for x is equal to 3, y is equal to 8. x is equal to 4 will not be considered since it is given that x is less than 4. So now let us check for reflexivity. Here we can see that 1, 1 does not belongs to r but 1 belongs to natural numbers. Therefore r is not reflexive. Now let us see the symmetric property of the relation. Now we can see that 1, 6 belongs to r but 6, 1 does not belongs to r. Therefore r is not symmetric. Now let us check for transitivity. We can see that 1, 6 belongs to r but there is no such ordered pair whose first element is therefore r is not transitive. Therefore we can see that r is not reflexive, r is not symmetric and r is not transitive. Hence the answer is neither reflexive, nor symmetric, nor transitive. I hope you have answered the question and enjoyed the session. Bye and have a nice day.