LetD be the set of all calendar dates from 4/30/1789 to 9/25/2014.

LetP be the set of names of U.S. presidents.

LetF be the set of names of first ladies of the U.S.

Consider the following two functionspres: D - Pwhere pres(d)is the name of the president of the U.S. on dated (the incumbent on inauguration days, to avoid ambiguity) andlady : P -F wherelady (p)is the name of the first lady of the U.S. during the presidency of president.

1. Can the compositionpres o ladybe defined? What about lady o pres?

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