Multiple choice

Let A be a set having 'n' elements. The number of binary operations that can be defined on A, is

  1. $n^{n^2}$
  2. $2^{n^n}$
  3. $n^{2^n}$
  4. $2^{2^n}$
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A Correct answer
Explanation

By definition, a binary operation defined on a set Y is a function $F : Y X Y \rightarrow ……..$ The domain, i.e. Y X Y has n × n elements (because Y has n elements). Each of ……… elements can be mapped to one of the 'n' elements of Y. So, totally $n^{n^2}$ binary is possible.

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