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Which claim is always true: L1 and L2 are regular languages, L = L1 - L2,...

Which claim is always true: L1 and L2 are regular languages, L = L1 - L2, then L

is finite

is regular

is complicated

is infinite
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Answer #1

If L1 and L2 are regular languages, then so is L1 – L2 = strings in L1 but not L2.

Proof: Let A and B be DFA’s whose languages are L and M, respectively. Construct C, the product automaton of A and B make the final states of C be the pairs, where A-state is final but B-state is not.

Observe that L1 - L2 = L1 ∩ L2'. We already know that regular languages are closed under complement and intersection. So, L1 - L2 will also be regular.

So L = L1 - L2 is regular.

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