Counting please show steps Let n 1 be a positive integer Ho

Counting, please show steps

Let n > 1 be a positive integer. How many functions f are there from the set {1,..., n}, to the set {0,1} such that: there are no restrictions. F assigns 0 to both 1 and n. f assigns 1 to exactly one number between 1 and n.

Solution

Ans(a):

if there is no restrictions then there can be uncountable functions as lots of rules can be made to map between both sets like Even-Odd case, divisor of a number etc.

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Ans(b):

there is no function possible for this case because function can\'t give different output (1 and n) for same input 0

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Ans(c):

Uncountable functions i think as

f assigns 1 to exactly one number means f(k)=1 where 1<k<n

it doesn\'t say anything about 0 so that can be used for any rule.