$(20$ points$)$ Consider the DFA below.

$($a$)$ Construct a two dimensional table where the row and column headers are the states of the above

DFA. Mark each cell with a $1($or a higher number representing the iteration number$)$ if the states

are $$different$.$ Unmarked cells will represent indistinguishable states.

$($b$)$ Construct a minimized DFA by collapsing $($groups of$)$ indistinguishable states into single states.& $12$ Aporns consuler be DFA halow