Suppose that A\displaystyle {A} and B\displaystyle {B} are sets such that AB={1,2}\displaystyle {A}\cap{B}={\left\lbrace{1},{2}\right\rbrace} and AB={1,2,3,4,5}\displaystyle {A}\cup{B}={\left\lbrace{1},{2},{3},{4},{5}\right\rbrace}. How many different sets are possible for A\displaystyle {A}? (Hint: list them all and then count!)