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 Nov10 awarded Popular Question Oct15 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. Oct13 comment Help with Subset Problem You will probably get a better response to your "follow up question" if you start a brand new question. Oct13 revised Help with Subset Problem added 376 characters in body Oct13 revised Help with Subset Problem added 376 characters in body Oct13 revised Help with Subset Problem added 376 characters in body Oct13 answered Help with Subset Problem Oct9 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. Oct6 answered How to prove a language is decidable Oct6 comment How to prove a language is decidable That is a much clearer explanation. I think you should edit your question with that information. Oct6 revised How to prove a language is decidable latex and clarification and title Oct6 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. Oct6 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? Oct6 suggested approved edit on How to prove a language is decidable Oct6 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 $s2$. Oct6 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? Oct6 comment How to prove a language is decidable What are S1 and S2? Are they subsets of the language $L(M)$ or strings of the language? Oct6 comment How to prove a language is decidable Should "s1 is subset of s2" be "s1 is substring of s2"? Sep30 awarded Explainer Sep15 comment Heuristics for solving first order, nonhomogenous, linear differential equations We haven't covered integrating factors yet, so I don't think this solution will be appropriate for my students.