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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

Mauro ALLEGRANZA
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    I commend to your attention the book Gödel, Escher, Bach, and specifically the MU puzzle. Think about the puzzle ("turn the string MI into the string MU using the given transformation rules") without looking at the solution. – Patrick Stevens Jul 11 '22 at 13:11
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    Because you have to devise all the steps of the process that produces it (if it is correctly produced). – Mauro ALLEGRANZA Jul 11 '22 at 14:02

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