Sampling and Signal Spectrum

Hi All,

I am new to DSP and I have a very basic question (Figure 13 of Rich
Lyons tutorial Quadrature sampling complex but not complicated) - When
we have a signal with center frequency f_0, why does sampling it with
frequency f_s and digitizing the signal result in the spectrum of the
signal being now centered at f_s  and - f_s?

I understand that multiplying two signals f_1 and f_2 results in two
signals with center freq. f_1+f_2 and f_1-f_2 ..
so isnt sampling is just like multiplying f_0 with a Impulse train f_s?

Thanks so much for the help,

Shravan.