Which reasoning correctly explains why P(X = c) = 0 for a continuous random variable with a well-defined pdf?

Because continuous random variables are deterministic and always take the same value, making the probability of any other single point zero while that single value is one.

Because a single point has zero width, the area under the pdf over that point is zero, and with infinitely many possible values, probability for any exact value is zero.

Because discrete approximations must be used to evaluate P(X=c), and those approximations always assign zero probability in the limit.

Because probability density at c must be zero for all continuous random variables; any nonzero density would violate the normalization condition.