SETS. please show work.
Let 
be the set of all calendar dates from 4/30/1789 to 9/25/2014.
Let 
be the set of names of U.S. presidents.
Let 
be the set of names of first ladies of the U.S.
Consider the following two functions 
where 
is the name of the president of the U.S. on date 
(the incumbent on inauguration days, to avoid ambiguity) and 
where 
is the name of the first lady of the U.S. during the presidency of president 
.
1. Can the composition 
be defined? What about 
?
2. Which of the following functional inverses exist and which do not?
, 
, 
,
