Question

Suppose we have the following Boolean function f:B^3 ==> B where f(x, y, z) = x(y + z). How can we determine the domain and range of this function?

Answer 1

The domain is given as B^3 -- any possible boolean triple is defined for x(y + z). The range is either true, false, or true/false. To find out, we can do a simple analysis (no need to construct a truth table).

f(x, y, z) = x(y + z) = xy + xz. So, if x is false, both terms are false, False is in the range. If x is true and y is true, xy is true, therefore xy + xz is true, so True is also in the range.