Question # 2 How many functions are there from the set {1 , 2 , . . . , n },where n is a positive integer, to the set{0 , 1}: a) that are one-to-one? b) that assign 0 to both 1 and n ? c) that assign...

Question # 2

How many functions are there from the set {1,
2, . . . , n},where
n
is a positive integer, to the

set{0,
1}:

1. 
   a)
   that are one-to-one?


2. 
   b)
   that assign 0 to both 1 and
   n?


3. 
   c)
   that assign 1 to exactly one of the positive integersless than
   n?