why is it hard to determine whether a given string belongs to $X$ or not for a set of strings $X$ is defined by an inductive definition

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I do not understand the answer to this question

Question: If a set of strings $X$ is defined by an inductive definition, then it is:

Answer: easy to generate elements of $X$ but hard to determine whether a given string belongs to $X$ or not

why would it be hard to determine a whether a given string belongs to $X$ or not, I cant seem to think of a reason why