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

  • $\begingroup$ Are the $x_i$ fixed? $\endgroup$ – Kai Nov 8 '18 at 21:48
  • $\begingroup$ I'm pretty sure they aren't fixed $\endgroup$ – Gabi G Nov 8 '18 at 21:55
  • 2
    $\begingroup$ 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 $f$? $\endgroup$ – Kai Nov 8 '18 at 22:06
  • $\begingroup$ @Kai This is an answer to the question. Post it as such? $\endgroup$ – Yuval Filmus Nov 8 '18 at 22:18
  • $\begingroup$ aww, did I give away too much? $\endgroup$ – Kai Nov 9 '18 at 10:43

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