Must be true. If there are any inspired musical performances, there must be sophisticated listeners in the audience. Taking the contrapositive gives us (A).

Could be false. If the audience isn’t treated to a good show, all we can infer is that there aren’t any inspired musical performances. We don’t know whether people who understand their musical roots are in the audience. (B) treats “understand musical roots” as sufficient for “good show,” when it’s only necessary.

This could be false. “Understand musical roots” isn’t sufficient for anything. Knowing that there are people in the audience who understand their musical roots tells us nothing about whether any musical performances are inspired.

Could be false. This says that if there people in the audience who understand their musical roots, the audience will be treated to a good show. This swaps the direction of the conditional chain in the stimulus. We don’t know whether understanding musical roots guarantees a good show. It might not.

Could be false. “Sophistical listeners” is only sufficient for “understand musical roots.” So having sophisticated listeners doesn’t tell us anything about whether there are inspired performances. Also, no condition is sufficient for “inspired musical performances.” So nothing would allow us to draw the inference that there are inspired performances.