# Relationship between Deterministic Finite Automata languages

What this "⊃" superset means? What do I need to prove here. Can someone, please, explain in English? Do I need to do a cross product? Plus, in textbooks and online I only see "∩" "∪" these kinda symbols. What this symbols "⊃" means?

Let M = (K, Σ, δ, s, F) be a deterministic finite automaton. Let M' =
(K, Σ, δ, s, F') be a similar deterministic finite automaton where F is
a proper
subset of F'. For each of the following provide an example to show that
the
relationship between L(M) and L(M') is possible or explain why the
relationship
is not possible.

The problem to prove: L(M) ⊃ L(M')

• "$L(M) \supset L(M')$" means exactly "$L(M') \subset L(M)$". Does it answer your question? – John L. Nov 30 '18 at 2:36
• I edited the question – optimus Nov 30 '18 at 2:41
• Logic symbols may be worth a read – candied_orange Nov 30 '18 at 3:39

In particular, "$$L(M) \supset L(M')$$" means $$L(M)$$ is a superset of $$L(M')$$, but $$L(M)$$ is not equal to $$L(M')$$. This is consistent with the explanation given by Wikipedia. To be more specific, it means all words in $$L(M')$$ are in $$L(M)$$, but at least one word is in $$L(M)$$ but not in $$L(M')$$.
A simple example of that situation can be the following. $$M'$$ is the finite automaton depicted at Wikipedia example with $$S_0$$ being the only accepting state. $$M'$$ accepts words with even number of 0's. Let $$M$$ be the same as $$M'$$ except that both states are accepting states. Then $$M$$ accepts all words.