Simplify this expression using Boolean identities 
 x(x'+y)

To simplify the Boolean expression \( x(x' + y) \), we can apply Boolean algebra rules and identities:

### Step 1: Apply the **Distributive Law**:
\[
x(x' + y) = xx' + xy
\]

### Step 2: Simplify using the **Complement Law**:
\[
xx' = 0
\]
This is because \( x' \) is the complement of \( x \), and \( x \cdot x' = 0 \).

### Step 3: Simplify the expression:
\[
0 + xy = xy
\]

### Final Simplified Expression:
\[
xy
\]

The simplified Boolean expression is \( xy \).

Would you like further explanation or details? 

Here are 5 related questions you can try:
1. Simplify the Boolean expression \( (x + x')(y + y') \).
2. What is the simplified form of \( (xy)' + x' \)?
3. Use Boolean identities to simplify \( (x + y)(x' + z) \).
4. How does the **Distributive Law** work in Boolean algebra?
5. What is the dual of the Boolean expression \( xy + x'z \)?

**Tip**: Always look for terms that can be eliminated using the complement or identity laws to simplify Boolean expressions quickly.

Simplify this expression using Boolean identities: x(x' + y)

Learn how to simplify the Boolean expression x(x' + y) using Boolean identities like the Distributive and Complement Laws. This step-by-step guide explains key logic concepts and is ideal for high school students in Grades 9-12.

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