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

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

Transcript text: Select the description that characterizes the Boolean expression: $x \bar{y} z$ Neither CNF nor DNF CNF, but not DNF DNF, but not CNF CNF and DNF

Solution

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.

Step 1: Analyze the Boolean Expression Structure

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.

Step 2: Determine if the Expression is in CNF

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.

Step 3: Determine if the Expression is in DNF

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

DNF, but not CNF

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