SETS. please show work.

/in /by

SETS. please show work.

Let D be the set of all calendar dates from 4/30/1789 to 9/25/2014.
Let P be the set of names of U.S. presidents.
Let F be the set of names of first ladies of the U.S.

Consider the following two functions pres:D rightarrow P where pres(d) is the name of the president of the U.S. on date d (the incumbent on inauguration days, to avoid ambiguity) and lady:P rightarrow F where lady(p) is the name of the first lady of the U.S. during the presidency of president p.

1. Can the composition pres circ lady be defined? What about lady circ pres?

2. Which of the following functional inverses exist and which do not?
pres^{-1}, lady^{-1}, (lady circ pres)^{-1},
(pres circ lady)^{-1}