Ekene T.

asked • 09/29/15

Can the composition pres o lady be defined? What about lady o pres?

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 o lady be 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

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