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The total number of boolean circuits formed will be equal to the total number of operation formed by that function.

Binary operation on set A is a function F: A  x  A $\rightarrow$ A.

the domain, i.e AxA has n X n elements, each of this n$ ^ {2}$ elements can be mapped to one of the elements of A.

so total $^{n^{n^{2}}}$ binary operation possible.

Hence the total boolean circuit  = $^{n^{n^{2}}}$
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