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Abstract Algebra

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More Counting Binary Operations

ABSALG-Y4CG3O

Let $B=B(X)$ be the set of binary operations on a finite set $X$ with $n$ elements.

How many binary operations can be defined on $B$?

A

$n^{n^{2n^2+2}}$

B

$n^{n^{2n^2}}$

C

$n^{2n^2}$

D

$n^9$

E

None of the above