Could someone please check my work?

7 Determine which of The Three properties (reflexive, Symmetric, and Transitive ) apply to each relation. ( a) Let R be The relation on IN given by XRy iff x dividesy. XRx : x divides x? Yes R is reflexive X X = 1 X Ry => yRx : x dividesy implies y divides x ? No, R is not Symmetric. Counterexample : x = 5, 4= 10 #5 / 10 but 10 1 5 ( X Ry n y Rz) = XRz : x dividesy and y divides z implies x divides zz Yes, R is transitive. Suppose xly and y/ z. Showx/z. Since x / 4, InEZ S. T. y=ny. .....-.> y is a multiple of x . > z is a multiple of y Since 4 / Z, FM E Z S.T. Z= my. Then Z = my = m (nx ) = (mn) x Imn ezz . .... . z is a multiple of Thus , X / z