Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$. Statement $I$: Change in internal energy of a system containing $n$ mole of ideal gas can be written as $\Delta U = nC_v(T_f - T_i) = \frac{nR}{\gamma - 1}(T_f - T_i)$, where $\gamma = C_p/C_v, T_i = $ initial temperature, $T_f = $ final temperature. Statement $II$: Relation between degree of freedom $f$ and $\gamma(= C_p/C_v)$ is $\gamma = 1 + \frac{2}{f}$. Choose the correct answer from the options given below.

• A
  Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
• B
  Both $A$ and $R$ are true but $R$ is $NOT$ the correct explanation of $A$.
• C
  $A$ is true but $R$ is false.
• D
  $A$ is false but $R$ is true.