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 Oct 27 awarded Popular Question Jul 16 awarded Notable Question Jul 1 awarded Yearling May 14 awarded Popular Question Nov 10 awarded Popular Question Oct 15 comment Help with Subset Problem @Extreme112 It's called Disjunction Introduction and explained in the other answers. I'll edit my answer to include the details. Oct 13 comment Help with Subset Problem You will probably get a better response to your "follow up question" if you start a brand new question. Oct 13 revised Help with Subset Problem added 376 characters in body Oct 13 revised Help with Subset Problem added 376 characters in body Oct 13 revised Help with Subset Problem added 376 characters in body Oct 13 answered Help with Subset Problem Oct 9 comment How to prove a language is decidable @DeepakMudiam No, you don't need to use the pumping lemma. You already know that $L(M)$ is regular because $M$ is a DFA. Oct 6 answered How to prove a language is decidable Oct 6 comment How to prove a language is decidable That is a much clearer explanation. I think you should edit your question with that information. Oct 6 revised How to prove a language is decidable latex and clarification and title Oct 6 comment How to prove a language is decidable Also, since $S_1$ is a subset of $S_2$, they must both be subsets of $L(M)$, not strings. Oct 6 comment How to prove a language is decidable If I understand the question correctly, you need to show that the language $L(M)$ with the given characteristics is decidable. Is this correct? Oct 6 suggested approved edit on How to prove a language is decidable Oct 6 comment How to prove a language is decidable Since $s1$ and $s2$ are strings, not sets, it makes no sense to say that $s1$ is a subset of $s2$. On the other hand, it does make sense to say that $s1$ is a substring of $s2$. Oct 6 comment How to prove a language is decidable Your question seems incomplete. A decidability problem must be stated in the form of a yes/no question. What is the question which you are trying to prove decidable?