Hey guys, I have a problem from my Topology course that I can't seem to figure out. Any help would be appreciated. Here it is:

The distance functions D'=D/(1+D) and D''= min{D,1} are each metrics on M. Let x M and letR>0.

Let:

S '(x)={y M|D'(x,y)< }

S ''(x)={y M|D''(x,y)< }

a) Prove that S ''(x) S '(x).

b)Prove that S '(x) S ''(x).

It almost seems to me like the containment should be switched in part a at least, but I don't know.

Thanks in Advance.