Question

Find DNF and CNF of the Boolean function f(x,y,z) for which f(x, y, z) = 0 if and only if (x + y)(y + z)(x + z) = 1​

Answer 1

Answer:

If you want to find DNF, you have to look at all rows that ends with T. When you find those rows, take the x,y, and z values from each respective column. Thus, you get

(x∧y∧z)∨(x∧¬y∧¬z)∨(¬x∧y∧¬z)∨(¬x∧¬y∧z).

Similarly, you can find CNF

(¬x∨¬y∨z)∧(¬x∨y∨¬z)∧(x∨¬y∨¬z)∧(x∨y∨z)