Questions: Select the description that characterizes the Boolean expression: x y̅ z Neither CNF nor DNF CNF, but not DNF DNF, but not CNF CNF and DNF

Solution Steps

To determine whether the Boolean expression \(x \bar{y} z\) is in Conjunctive Normal Form (CNF) or Disjunctive Normal Form (DNF), we need to understand the structure of these forms. CNF is a conjunction of disjunctions, while DNF is a disjunction of conjunctions. The given expression is a single conjunction of literals, which fits the definition of DNF but not CNF.

The given Boolean expression is \(x \bar{y} z\). This expression is a conjunction of literals, where \(x\), \(\bar{y}\), and \(z\) are combined using the AND operation.

Conjunctive Normal Form (CNF) is characterized by a conjunction of disjunctions. Each clause in CNF is a disjunction (OR operation) of literals. Since the given expression is a single conjunction without any disjunctions, it does not fit the CNF structure.

Disjunctive Normal Form (DNF) is characterized by a disjunction of conjunctions. Each term in DNF is a conjunction (AND operation) of literals. The given expression \(x \bar{y} z\) is a single conjunction of literals, which fits the DNF structure.

Final Answer