Please break this down into explained steps as if I am a 5 year old. Assume that

Question

Please break this down into explained steps as if I am a 5 year old. Assume that I am easily confused - over explain it please.

Please do not simply say "this is undefined" explain specifically why that is so.

I really need this to be broken down into thoroughly explained steps.

Such as saying "multiply this by this, because of this reason" Draw arrows if you think it will help explain, I really need to comprehend the process. Presume I have extreme difficulty.

Please overly explain how you come to any answer.

Let D be the set of all calendar dates from 4/30/1789 to 9125/2014. 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 Let D be the set of all calendar dates from 4/30/1789 to 9/25/2014 is the name 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 aboutlady o pres? 2. Which of the following functional inverses exist and which do not? pres lady lady o pres)1 (pres o lady)

Explanation / Answer

Ans(1):

we know that (fog)(x) means f(g(x)) means output of g(x) is input of f(x)
now consider the same logic in
(press o lady)(p)
which means press( lady (p))
lady(p) i.e. function lady : P->F gives output of first lady say "l" during presidency of president p
so press( lady (p)) changes into press( l)
while input of press(d) should be some date "d" as per definition of press: D->P.

Hence (press o lady) is not defined.
----------------------
Now let's check for (lady o press)
(lady o press)(d)
which means press lady( press(d))
press(d) i.e. function press: D->P gives output of the name of president say "p".
so lady( press(d)) changes into lady(p)
Input of lady(p) is "p" which is same as per given definition of lady : P->F

Hence (lady o press) is defined.

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