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Find minimal dfa's for the following languages. In each case prove that the result is minimal.

(1) L = {a n bm> :n≥2,m≥1}.

(2)L = {a n :n ≥ 0,n ≠ 3}

(3) L = {a n :n mod 3 = 0}∪{a n : n mod 5 = 1}

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