Both statements are true, but one describes what an oscilloscope does and the other what limits it — a limitation is not an explanation of a capability. Option 2.

The assertion is the instrument's definition. An oscilloscope plots voltage against time: the vertical amplifier deflects the trace in proportion to the input while the timebase sweeps it horizontally at a known rate, so what appears is the waveform itself — rise time, overshoot, ringing, duty cycle, glitches. That is what distinguishes it from a voltmeter, which collapses the whole waveform into a single number.

The reason is also true. Bandwidth is the headline specification of any scope, defined as the frequency at which a sine wave's displayed amplitude has fallen by 3 dB — to 70.7 % of its true value. Above that the instrument understates what it is shown.

How bandwidth limits what can be trusted. For a scope with a Gaussian response the rise time follows

\(t_{r}\approx\dfrac{0.35}{BW}\)

so a 100 MHz instrument cannot display an edge faster than about 3.5 ns. Worse, the measured rise time is the combination of signal and instrument:

\(t_{measured}=\sqrt{t_{signal}^{2}+t_{scope}^{2}}\)

which is why the usual rule is to choose a scope with three to five times the bandwidth of the fastest edge of interest. A square wave needs several odd harmonics to keep its shape, so a 100 MHz square wave viewed on a 100 MHz scope appears as a sine.

Why the two statements do not connect. The reason would explain the assertion only if bandwidth were the cause of the graphical display. It is not: bandwidth constrains how faithfully the graph is drawn. The instrument would still plot voltage against time if its bandwidth were ten times larger or ten times smaller. Both sentences are correct and both are about oscilloscopes, which is precisely the situation option 2 describes.

Other limitations deserve mention alongside it — sample rate and memory depth on a digital scope, vertical resolution of eight bits on most, probe loading, and the trigger's own bandwidth — none of which explains the assertion either.

Hence, both are true, but (R) is not the correct explanation of (A).