Question: Functions are a special kind of relation. A function f : A A is friendly if a A , f ( a ) = a

Functions are a special kind of relation. A function f : A A is "friendly" if aA,f(a)=a .Let A be a set with| A|=n.

(a)Assume n is even. How many symmetric relations are there on A A that are also friendly functions?

(b)What if n is odd? How many symmetric relations are there on A A that are also friendly functions in this case?

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