For each exercise, you must first build the most

concise DFA for each given language $(2$ points each$),$ then build the DFA that recognizes the intersection of the

two languages using EXACTLY the algorithm we discussed in class $(8$ points$),$ and provide a concise regular

expression for this language $(3$ points$)1$a$.($a $+)*$a $1$b$.($a $+$ b$)*$aa$($a $+$ b$)*2$a$.($b $+$ ab$)*($a $+^)2$b$.($b $+$ ba$)*$a