Both statements are true, and the wider bandwidth is genuinely the source of the higher fidelity, so the code is 1.

Bandwidth buys fidelity in two distinct ways.

First, a wider audio range. FM broadcasting allocates 200 kHz per channel and transmits audio up to 15 kHz, against AM's 10 kHz channel carrying audio limited to about 5 kHz. The difference is immediately audible — AM simply cannot carry the top two octaves of music.

Second, and more fundamentally, an improved signal-to-noise ratio. The output SNR of an FM receiver improves with the square of the modulation index:

\(\left(\dfrac{S}{N}\right)_{o}=3\beta^{2}\left(\beta+1\right)\left(\dfrac{S}{N}\right)_{i}\)

and since Carson's rule gives

\(B=2\left(\Delta f+f_{m}\right)=2f_{m}\left(\beta+1\right)\)

a larger β means both a larger bandwidth and a better SNR. Bandwidth is being traded for noise performance — the classic exchange that Shannon's capacity formula formalises. With \(\Delta f=75\ \text{kHz}\) and \(f_{m}=15\ \text{kHz}\), broadcast FM runs at \(\beta=5\) and gains roughly 15 to 20 dB over AM for the same received power.

The third mechanism is that amplitude noise carries no information in FM. Since the message rides on frequency, a limiter can clip the received signal to constant amplitude and discard impulse noise, lightning and ignition interference entirely — something AM cannot do without destroying the message.

Pre-emphasis and de-emphasis add a further few decibels: because FM noise rises with modulating frequency, the transmitter boosts the treble by a 50 μs (or 75 μs) time constant and the receiver applies the exact inverse, restoring the balance while pushing the noise back down.

The cost of all this is spectrum. Twenty AM stations fit in the space of one FM channel — which is why AM survives for long-range, low-fidelity broadcasting and FM occupies the VHF band, where bandwidth is plentiful but range is limited to line of sight.

Hence, both (A) and (R) are true and (R) is the correct explanation of (A).