To design a logic circuit for the given expression $AB'C + BC + AB'C$, we first simplify it:

1. The expression is: $AB'C + BC + AB'C$
2. Notice that $AB'C$ appears twice. We can simplify the expression to: $AB'C + BC$

This is the simplified Boolean expression. Now let's break it down:

• $AB'C$ consists of three variables where $A$ and $C$ are ANDed with the complement of $B$.
• $BC$ is a simple AND gate between $B$ and $C$.

Steps to design the logic circuit:

1. AND Gates:

   • One AND gate for $AB'C$: Input $A$, $B'$ (complement of $B$), and $C$.
   • Another AND gate for $BC$: Input $B$ and $C$.

2. OR Gate:

   • The output of both AND gates will feed into an OR gate to produce the final output.

Now, I'll describe the layout for the circuit:

• Inputs: Three inputs $A$, $B$, and $C$.
• NOT Gate: The input $B$ passes through a NOT gate to create $B'$ for the $AB'C$ term.
• AND Gate 1: Takes $A$, $B'$, and $C$ as inputs and outputs $AB'C$.
• AND Gate 2: Takes $B$ and $C$ as inputs and outputs $BC$.
• OR Gate: Combines the outputs of both AND gates to get the final output $AB'C + BC$.

Would you like an illustration of the circuit? Also, here are some related questions:

1. How do AND, OR, and NOT gates function in Boolean algebra?
2. What are some common techniques for simplifying Boolean expressions?
3. How does De Morgan's Law apply to logic circuits?
4. What are some practical applications of logic circuits in real-world systems?
5. How would you convert this logic circuit into a truth table?

Tip: When simplifying Boolean expressions, always look for common terms to reduce redundancy and optimize the logic circuit.