Another way to find a Boolean expression that represents a Boolean function is to form a Boolean product of Boolean sums of literals. Exercises 1–5 are concerned with representations of this kind.
1. Find a Boolean sum containing either x or 
either y or and either z or 
that has the value 0 if and only if
a) x = y = 1, z = 0.
b) x = y = z = 0.
c) x = z = 0, y = 1.
2. Find a Boolean product of Boolean sums of literals that has the value 0 if and only if x = y = 1 and z = 0, x = z = 0 and y = 1, or x = y = z = 0.
3. Show that the Boolean sum y1+ y2+· · ·+yn, where yi = xior yi = xi, has the value 0 for exactly one combination of the values of the variables, namely, when xi = 0 if yi = xiand xi = 1 if yi = xi. This Boolean sum is called a maxterm.
4. Show that a Boolean function can be represented as a Boolean product of maxterms. This representation is called the product-of-sums expansion or conjunctive normal form of the function.
5. Find the product-of-sums expansion of each of the Boolean functions in Exercise 6.
Exercise 6 Find the sum-of-products expansions of these Boolean functions.
a) F(x, y, z) = x + y + z
b) F(x, y, z) = (x + z)y
c) F(x, y, z) = x
d) F(x, y, z) = x y