Question

7 multiple choice 1 point select the description that characterizes the boolean expression: $x(\overline{y}+z)$ cnf, but not dnf neither cnf nor dnf dnf, but not cnf cnf and dnf 8 multiple choice 1 point select the description that characterizes the boolean expression: $(x + y)(\overline{u}+z)$ cnf, but not dnf dnf, but not cnf neither cnf nor dnf cnf and dnf 9 multiple choice 1 point select the expression that is equivalent to $xy+\overline{z}+\overline{u}$. $\overline{\overline{xy}\overline{z}\overline{u}}$ $\overline{xyzu}$ $\overline{\overline{xy}\overline{z}u}$ $\overline{xyzu}$

Explanation:

Question 7

Step1: Recall CNF and DNF definitions

Conjunctive - Normal - Form (CNF) is a product of sums, and Disjunctive - Normal - Form (DNF) is a sum of products. The expression $x(\overline{y}+z)$ is a product of $x$ and $(\overline{y} + z)$. It is in CNF (product of sums) and not in DNF (it's not a sum of products).

Step1: Analyze the form

The expression $(x + y)(\overline{u}+z)$ is a product of sums ($x + y$ and $\overline{u}+z$). It is in CNF. It is not in DNF since it's not a sum of products.

Step1: Apply De - Morgan's law

De - Morgan's law states that $\overline{a + b}=\overline{a}\overline{b}$ and $\overline{a\cdot b}=\overline{a}+\overline{b}$. For the expression $xy+\overline{z}+\overline{u}$, by De - Morgan's law, $\overline{\overline{xy}\cdot z\cdot u}=\overline{\overline{xy}}+\overline{z}+\overline{u}=xy + \overline{z}+\overline{u}$.

Answer:

A. CNF, but not DNF

Question 8