Given below are two statements:
Statement $I$: The graph of $t_{1/2}$ versus initial concentration $[R]_0$ for a first-order reaction is a horizontal line.
Statement $II$: The graph of $\log \frac{[R]_0}{[R]}$ versus time $t$ for a first-order reaction is a straight line passing through the origin with a slope equal to $\frac{k}{2.303}$.
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
  Both Statement $I$ and Statement $II$ are true
• D
  Statement $I$ is true but Statement $II$ is false