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2 0 points In the videos and the text, you saw that regular languages are closed under the union operation i . e . ,

20 points In the videos and the text, you saw that regular languages
are closed under the union operation i.e., if L1 and L2 are both
regular, then L1\cup L2 is regular. There were 2 proofs. In both proofs,
we built a machine from 2 DFAs M1 and M2, where L(M1)= L1 and
L(M2)= L2. The first proof constructed a new DFA and the second
constructed and NFA. (Recall that if and only if proofs have 2 parts
the if part and the only if part.)
Describe how to modify the DFA construction to prove that regular
languages are closed under intersection. Argue that your modified con-
struction is correct. Specifically, prove that w in L1\cap L2 if and only if
w is accepted by your constructed DFA

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