[Solved]: If $L = L(M)$ then $L$ is a subset of $L(M)$ and $L(M)$ is a subset of $L$

Problem Detail: 

If $L = L(M)$ then $L$ is a subset of $L(M)$ and $L(M)$ is a subset of $L$.

Can anyone clarify what does this mean?

Asked By : makakas

Answered By : Hendrik Jan

This is just a set-theoretical equality. Two sets are equal precisely when they are included in one another: $A = B$ iff $A\subseteq B$ and $B\subseteq A$. The notation is applied in the context of languages of automata. In order to show an automaton $M$ defines language $L$, you have to show it accepts all strings from $L$, and no more than those strings.

Basic, when doing automata and language theory, I am afraid.

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Question Source : http://cs.stackexchange.com/questions/11643