Need math help with a composition

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)

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Need math help with a composition

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