Discussion
Why must an anti-aliasing filter precede the sampler rather than follow it?
Answer: B
Because aliasing is irreversible. Once a component above half the sampling rate has folded down, it occupies exactly the same frequency as a legitimate component and no subsequent processing can tell them apart or separate them. The only remedy is to remove the offending energy before the fold happens, which is what the anti-alias filter does. Filters operate on discrete-time signals perfectly well, which is the whole of digital filtering, so the third option is simply false. Nothing damages the filter. And a delay is a benign and correctable effect, quite unlike an irreversible loss of information.
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