how many boolean functions exist that satisfy the condition : $Not[f(x_1,x_2,x_3,....,x_n)]$ = $f(Not(x_1), Not(x_2),...,Not(x_n))$

  • Are the $x_i$ fixed? – Kai Nov 8 at 21:48
  • I'm pretty sure they aren't fixed – Gabi G Nov 8 at 21:55
  • 2
    It's a counting exercise. Realise that whenever you choose $f(x_1,\ldots , x_n) = b$ for fixed $x_1,\ldots , x_n$, you fix $f(\neg x_1,\ldots , \neg x_n) = \neg b$. So how many choices do you have to make to fully determine $f$? – Kai Nov 8 at 22:06
  • @Kai This is an answer to the question. Post it as such? – Yuval Filmus Nov 8 at 22:18
  • aww, did I give away too much? – Kai Nov 9 at 10:43

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