# On the relations between rank and torsion of homology and cohomology of a CW pair.

I am reading Massey's book on algebraic topology and on the chapter of universal coefficient theorem of cohomology, there is this exercise 4.1 that I don't know how to solve.

Let (X,A)be a pair such that $H_n(X,A)$ is a finitely generated abelian group.

Prove rank$(H^n(X,A;\mathbb{Z})) = \text{rank}(H_n(X,A))$,Torsion$(H^n(X,A;\mathbb{Z})) \cong \text{Torsion }(H_{n-1}(X,A))$.

I wonder is this a corollary of the universal coefficient thereom? If so, how do we compute Tor(Ext($H_n(X,A)$))?