Given below are two statements:
Statement-$I$: $A$ speech signal of $2 \, kHz$ is used to modulate a carrier signal of $1 \, MHz$. The bandwidth requirement for the signal is $4 \, kHz$.
Statement-$II$: The sideband frequencies are $1002 \, kHz$ and $998 \, kHz$.
In the light of the above statements,choose the correct answer from the options given below:

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