Question

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?

Answer 1

Hey,

If n = 1 then there are two choices for the first and only element in the domain. So, we have 2 functions if n = 1.

If n = 2 then there are two choices for the first element in the domain. Then, since one choice is taken there is one choice for the second element in the domain. So, we have 2 * 1 = 2 functions if n = 2.

If n >= 3 then there will always be elements in the domain with no images to map to. So, we have 0 functions if n >= 3.

HOPE IT HELPS YOU:-))

Answer 2

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