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## Homework Statement

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 1 to exactly one of the positive integers less than n?

## Homework Equations

## The Attempt at a Solution

Since every element in the domain {1, 2, . . . , n} has two options in the codomain {0, 1} there a total of 2^n functions from the domain to the codomain.

Also, I understand that to be a one-to-one relationship no element of the codomain is the image of more than one element in the domain.

However, I'm unsure how to solve the problems. Any suggestions would be appreciated.