Chapter 12.1, Problem 30E

Show that ifFandGare Boolean functions represented by Boolean expressions in n variables andF=G, thenF^dandG^d, whereF^dandG^dare the Boolean functions represented by the duals of the Boolean expressions representingFandG, respectively.

[Hint: Use the result of Exercise 29.]

*29. Suppose thatFis a Boolean function represented by a Boolean expression in the variablesx₁...,x_n. Show that

   $F^d\left(x_1,\mathrm{...},x_n\right)=\overline{F\left(\stackrel{¯}{x_1},\mathrm{...},\stackrel{¯}{x_n}\right)}$