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. presidents. Let F be the set of names of first...

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 → 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 → 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 ○ lady be defined? What about lady ○pres?

2. Which of the following functional inverses exist and which do not?

pres-1, lady-1, (lady ○pres)-1, (pres ○lady)-1