https://file.aiquickdraw.com/mathbot/file/17264820216144kl3qyh4.pdf

From the document you uploaded, I see that your task involves simplifying logic circuits using Boolean algebra rules. Here are the steps to complete the tasks mentioned in the document:

### Task 1: Simplify the Expression
You are required to simplify the following Boolean expressions and build the circuit based on the simplified results, followed by constructing a truth table:

#### Expression 1:
\[
X = A \cdot (A + B + C)
\]

**Solution:**
1. Apply **Absorption Law** (Rule 10): \( A \cdot (A + B) = A \).
   \[
   X = A
   \]
   The simplified expression for \( X \) is \( A \).

2. **Truth Table**:
   - If \( A = 1 \), then \( X = 1 \).
   - If \( A = 0 \), then \( X = 0 \).

---

#### Expression 2:
\[
X = (A \cdot B) + (C \cdot D \cdot A)
\]

**Solution:**
1. Factor \( A \) out from both terms:
   \[
   X = A \cdot (B + C \cdot D)
   \]

This is the simplified expression.

2. **Truth Table**:
   You can now construct the truth table based on the simplified form \( X = A \cdot (B + C \cdot D) \).

---

### Task 2: Simplify the Circuit in Figure 3-3
You are also tasked with simplifying a given circuit (refer to "Gambar 3-3"). Based on Boolean simplifications, simplify the logic gate arrangement and compare the truth tables before and after simplification.

Would you like detailed explanations or any help with circuit diagrams?

---

Here are 5 related questions that might help you expand your understanding:
1. What is the role of De Morgan's laws in simplifying Boolean expressions?
2. How does the truth table change when you simplify a logic circuit?
3. Can every logic circuit be simplified using Boolean algebra?
4. How would the circuit for Expression 2 change after simplification?
5. What are the key differences between logic circuit simplifications before and after simplification?

**Tip**: Always apply the **Absorption** and **Distribution** rules when simplifying complex Boolean expressions.

Learn how to simplify logic circuits using Boolean algebra. This problem involves applying Boolean algebra rules like Absorption and De Morgan's Theorems to simplify expressions and logic circuits. Suitable for college-level students studying digital electronics.

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