SOLUTION: Can I please have your assistance? 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 fir

Algebra ->  Inverses -> SOLUTION: Can I please have your assistance? 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 fir      Log On


   

Question 1040392: Can I please have your assistance? 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 arrow 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 arrow F where lady (p) is the name of the first lady of the U.S. during the presidency of president p. Question: Which of the following functional inverses exist and which do not? pres -1, lady -1 (lady o pres) -1, (pres o lady) -1
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
(pres o lady)-1 or %28pres%28lady%29%29%5E%28-1%29 will not exist, because pres o lady is undefined.

(lady o pres)-1 or %28lady%28pres%29%29%5E%28-1%29 exists, because any first lady can be matched to only one presidential inauguration date (of her president husband.)
%28lady%29%5E%28-1%29 exists, because any first lady can be matched to only one president (who is her husband). (No first lady was ever a wife to two
different presidents.)
%28pres%29%5E%28-1%29 exists, because any president can be matched to exactly one inauguration date. (No president has two inauguration dates, at
least in theory...)