Recently I've been trying to figure out what's the point of negative frequencies produced by the fourier transform. One answer was it's just there to make calculations more elegant. It could be anything on the negative part of the $w$ axis, but we've chosen to make it an even function. If we used fourier sine transform for example, there would be no negative frequency values at all. Now recall what Nyqist-Shannon theorem says about what's the necessary minimum sampling frequency to avoid aliasing. It has to be at least twice as big as the maximum frequency present in sampled signal.
What if we got rid of the negative frequencies? We would only have only the positive ones that make any sense. 
Now in b) we can sample at frequency $f_s = B$ and avoid aliasing, because we don't have the negative frequencies that would cause aliasing. So we can sample the signal at 2 times higher frequency than it's possible with presence of negative frequencies in a).
Could you please tell me at which point my reasoning is wrong here? What's the motivation for having a fourier spectrum of a signal satisfy $X(f)=X(-f)$?