Consider the Boolean expression A(x, y, z) = x (y'z)’. Which of the following is the complete sum-of-products form of the given Boolean expression?

Correct option is D

We are asked to find the complete sum-of-products form of the given Boolean expression: A(x, y, z) = x (y' z)'
Let’s break down this expression and simplify it step by step.
Step 1: Simplify the expression A(x, y, z) = x (y' z)'
We begin by applying De Morgan's law to the expression (y' z)'. According to De Morgan’s law:
(y′z)′ = y + z′
This gives us the expression:
A(x, y, z) = x (y + z')
Step 2: Expand the Expression
Now, using the distributive property, we expand the expression:
​$$A(x, y, z) = x \cdot y + x \cdot z'$$​​
Construct the Truth Table
Now, let's construct the truth table to find the rows where A = 1: The table shows the values of x, y, z, and the corresponding values of A(x, y, z), where A = 1 for the rows:

For A = 1, the corresponding rows are:
· x = 1, y = 0, z = 0 → minterm: x y'z'
· x = 1, y = 1, z = 0 → minterm: x yz'
· x = 1, y = 1, z = 1 → minterm: x yz
Thus, the complete sum-of-products form is:
A(x, y, z) = xyz + xy'z' + xyz'