Recursive Set
Need a Solution to the following question
Let $\Sigma$ be the alphabet defined as follows: $\Sigma = {e, l, v}$. We now deifine the set of strings P according to the following:
BASIS STEP: If $x \in \Sigma $ then $x \Sigma P$.
RECURSIVE STEP: If $\omega \in P$ and $x \in \Sigma $, then $x \omega x \in P$.
Show that the string level is in P

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Answer
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Will greatly appreciate if you could please provide step by step full answer, and please solve it in a way that someone who semi-understands (me) can comprehend and study it in the future.
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There is nothing more to say, the answer is as full as it can get.
The answer is accepted.
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Thanks for replying Please provide full answers, and please solve them in a way that a someone who semi-understands (me) can comprehend and study it in the future.