Chapter 3, Problem 10E

a.

Explanation of Solution

Given:

$\text{x = x}\cdot \text{y + x}\cdot \text{y' }$

Truth table for the above expression:

x

y

y’

x∙y

x∙y’

b.

Program Plan Intro

Distributive law:

Consider three variables x, y, and z. The multiplication of variable (x) with the sum of two variables (y and z) is same as the sum of the products (xy and xz).

The representation of distributive law is as follows:

$\begin{array}{l}\text{x + (y}\cdot \text{z) = (x + y) (x + z)}\\ \text{x (y + z) = x}\cdot \text{y + x}\cdot \text{z}\end{array}$

Inverse law:

The sum of the variable (x) and the complement of the variable (x’) is 1 and the product of the variable (x) and the complement of the variable (x’) is 0.

The representation of inverse law is as follows:

$\begin{array}{l}\text{x + x' = 1}\\ \text{x }\cdot \text{ x = 0}\end{array}$

Identity law:

The sum of the variable (x) and the value 0 is “x” and the product of the variable (x) and the value 1 is “x”.

The representation of inverse law is as follows:

$\begin{array}{l}\text{0 + x = x}\\ \text{1 }\cdot \text{ x = x}\end{array}$