Let $p : (\widetilde X, \widetilde {x_0}) \longrightarrow (X,x_0)$ be a covering map where $\widetilde X$ is path connected and let $p_{*}$ be the induced homomorphism under $p$. Then show that the index of $p_{*} (\pi_{1} (\widetilde X, \widetilde {x_0}))$ in $\pi_{1} (X,x_0)$ is same as that of the cardinality of $p^{-1} (x_0)$.
How can I proceed? Please help me in this regard.
Thank you very much.