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 press : 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 (the -1 should be in superscript)