text: can u help me its urgent ? for arbitrary strings x and y, show that (xy)r = yr • xr , where, by notation zr is the string obtained by reversing the string z. we define the reverse fnction as reverse(x.a)=a.x where a belongs to the alphabet set. we prove by induction that  reverse(xy) = reverse(y). reverse(x) basis:  let y = l(lambda the empty string) reverse(xy)=reverse(x.l) =l.reverse(x) =reverse(l).reverse(x)  induction step: let the induction hypothesis is  reverse(xz) = reverse(z).reverse(x) now let y = z.a where a belongs to alphabet set. so y>z; so from defination reverse(y)=reverse(z.a) =a.reverse(z)....(1) now reverse(xy)=reverse(x.(z.a)) reverse((x.z).a)=a.reverse(x.z) =a.reverse(z).reverse(x) [from induction hypothesis.] =reverse(y).reverse(x)[from 1] hence proved..