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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 $A$

  1. Give the expression for $N_r,$ in terms of $n.$
  2. Give the expression for $N_f,$ terms of $n.$
  3. Which is larger for all possible $n,N_r$ or $N_f$
in Set Theory & Algebra retagged by
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A relation on a set S={1,2,3} → {(1,2),(1,3)} this is a relation but not a function.

Every function is a relation but converse is false.
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5 Answers

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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.

edited by

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