I am seeking to understand Rings of Fractions and Fields of Fractions - and hence am reading Dummit and Foote Section 7.5

Exercise 3 in Section 7.5 reads as follows:

Let F be a field. Prove the F contains a unique smallest subfield $\displaystyle F_0 $ and that $\displaystyle F_0 $ is isomorphic to either $\displaystyle \mathbb{Q} $ or $\displaystyle \mathbb{Z/pZ} $ for some prime p. (Note: $\displaystyle F_0 $ is called prime subfield of F.)

Can anyone help with this exercise.

Peter