Let $R$ be an integral domain and $M$ a finitely generated $R$-module. Show that $rank(M/Tor(M))$=$rank(M)$

I only need item b).  Full question:

Let $R$ be an integral domain and $M$ a finitely generated $R$-module.

  • a) Show that $M/Tor(M)$ is free of torsion. (ALREADY PROVEN) ?
  • b) Show that $rank(M/Tor(M))$=$rank(M)$.
Again, I've already shown item a). Just announced it in case it's needed.

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