Suppose that A\displaystyle {A} and B\displaystyle {B} are sets such that AB={4,7}\displaystyle {A}\cap{B}={\left\lbrace{4},{7}\right\rbrace} and AB={1,3,4,7,8,9,10}\displaystyle {A}\cup{B}={\left\lbrace{1},{3},{4},{7},{8},{9},{10}\right\rbrace}. How many different sets are possible for A\displaystyle {A}?