Given below are two statements:
Statement $I$: There are several conformers for $n$-butane. Out of those conformers, the fully eclipsed conformer (dihedral angle $0^{\circ}$) is the least stable and the anti-staggered conformer (dihedral angle $180^{\circ}$) is the most stable.
Statement $II$: As the dihedral angle increases from $0^{\circ}$ to $60^{\circ}$, torsional strain decreases from the fully eclipsed conformer $(X)$ to the gauche conformer $(Y)$.
In the light of the above statements, choose the correct answer from the options given below:

• A
  Both Statement $I$ and Statement $II$ are false
• B
  Statement $I$ is false but Statement $II$ is true
• C
  Statement $I$ is true but Statement $II$ is false
• D
  Both Statement $I$ and Statement $II$ are true