Let $A$ be a set of $n(>0)$ elements. Let $N_r$ be the number of binary relations on $A$ and let $N_f$ be the number of functions from $A$ to $A$
x wrong
you cannot do like this bcz it is For all n - so you can't apply asymptotic method as it's only meant for all "sufficiently large" n.
this method is wrong.
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