title: Construct a DFA for the following language: all strings that have at least three 0s and at most two 1s
body: <p>I am to construct a DFA from the intersection of two simpler DFAs.  The first simpler DFA recognizes languages of all strings that have at least three 0s, and the second simpler language DFA recognizes languages of strings of at most two 1s.  The alphabet is (0,1).  I'm not sure how to construct a larger DFA combining the two.  Thanks!</p>