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(a) Construct a DFA for the following languages over alphabet {0,1} : L= set of all strings w such that numbers of 1 's in

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(a) Construct a DFA for the following languages over alphabet {0,1} : L= set of all strings w such that numbers of 1 's in w is 3mod4 (b) Prove the following: (i) +0(100)(0(100))=(0+100) (ii) P+PQQ=abQ where P=b+aab and Q is any regular expressi

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