In the case of amplitude modulation to avoid distortion the modulation index $$\mu$$ should be:

In amplitude modulation (AM), the modulated wave can be expressed as:

where $$\mu$$ is the modulation index defined as:

Here, $$A_m$$ is the amplitude of the message signal and $$A_c$$ is the amplitude of the carrier signal.

For the modulated signal to be free from distortion (i.e., the envelope of the modulated wave should faithfully reproduce the message signal), we need:

If $$\mu > 1$$, the modulated wave undergoes over-modulation, leading to distortion of the signal during demodulation. The envelope of the carrier no longer faithfully follows the modulating signal.

If $$\mu = 0$$, there is no modulation at all, so no information is transmitted.

Therefore, the correct answer is Option A: $$\mu \leq 1$$.