Number of functions from one set to another

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?

For a) my answer is 2 if n = 1 or n = 2 and 0 if n > 2.
But I'm stuck on both b) and c). Any help would be appreciated.

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Originally Posted by nicnicman

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?
For a) my answer is 2 if n = 1 or n = 2 and 0 if n > 2.
But I'm stuck on both b) and c). Any help would be appreciated.

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There are a total of functions .

b) The answer is if , or if .

Now, you reply with an explication. If you do we can help with c).

Well, that's the hard part (the answer's in the back of the book), but I'll work on it.

Thanks.

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Originally Posted by nicnicman

Well, that's the hard part (the answer's in the back of the book), but I'll work on it.

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Well that I suggest that you draw diagrams.
Do it for n=2,3,4,5.
Say

Draw lines from 1 & 5 to 0. How many ways can you map the 2, 3, & 4?

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How many ways can you map the 2, 3, & 4?

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3; 2 to 1, 3 to 1, and 4 to 1

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Originally Posted by nicnicman

3; 2 to 1, 3 to 1, and 4 to 1

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Now I understand your problem: you simply do not understand what this is all about

is the correct answer.

Your difficulty requires live sit-down help. Please see your instructor.