Chapter 12, Problem 22SE

A Boolean function that can be represented by a threshold gate is called a threshold function. Show that each of these functions is a threshold function.

a) F (x) =

$\bar{x}$ .

b) F (x, y) = x + y

c) F (x, y) = xy

d) F (x, y) = x|y

e) F (x, y) = x?y

f) F (x, y, z) = x + yz

g) F (w, x, y, z) = w + xy + z

h) F (w, x, y, z) = wxz + x $\bar{y}$ z