The given Boolean expression is:

$A + \overline{A}B + \overline{B}C$

Here, $A$, $B$, and $C$ are the variables. Let's create the truth table for the expression step by step.

Step 1: Identify Intermediate Columns

We'll calculate intermediate expressions:

1. $\overline{A}$ (NOT $A$)
2. $\overline{A}B$ (AND of $\overline{A}$ and $B$)
3. $\overline{B}$ (NOT $B$)
4. $\overline{B}C$ (AND of $\overline{B}$ and $C$)
5. Finally, $A + \overline{A}B + \overline{B}C$ (OR of $A$, $\overline{A}B$, and $\overline{B}C$).

Step 2: Truth Table

Here is the full truth table for the expression:

Explanation of the Last Column

The final column ($A + \overline{A}B + \overline{B}C$) is the result of combining:

• $A$ (directly from the input)
• $\overline{A}B$ (when $A = 0$ and $B = 1$)
• $\overline{B}C$ (when $B = 0$ and $C = 1$).

Let me know if you would like detailed steps for each row or further clarifications!

Questions for Exploration:

1. What is the significance of the complement ($\overline{A}$ or $\overline{B}$) in Boolean expressions?
2. How can we simplify the given Boolean expression using Boolean algebra rules?
3. Can we draw the logic circuit for this Boolean expression?
4. How does the truth table help in verifying logical equivalences?
5. How is this Boolean expression used in practical applications, like digital logic?

Tip:

When solving complex Boolean expressions, always break them into smaller parts and solve step by step using a truth table for clarity.