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The truth table you've provided is for the Boolean expression \( F(x, y, z) = x + yz \). Let's complete the truth table based on this expression.

### Boolean Expression Breakdown:
- \( F(x, y, z) = x + yz \)
- \( x + yz \) means that the output is true if either \( x \) is true or both \( y \) and \( z \) are true.

We will calculate the result for each combination of \( x \), \( y \), and \( z \).

| \( x \) | \( y \) | \( z \) | \( x + yz \) |
|--------|--------|--------|-------------|
|   1    |   1    |   1    |     1       |
|   1    |   1    |   0    |     1       |
|   1    |   0    |   1    |     1       |
|   1    |   0    |   0    |     1       |
|   0    |   1    |   1    |     1       |
|   0    |   1    |   0    |     0       |
|   0    |   0    |   1    |     0       |
|   0    |   0    |   0    |     0       |

### Explanation:
- For the first four rows, \( x = 1 \), which directly makes \( F = 1 \) (since \( x + yz = 1 \)).
- For the fifth row, \( x = 0 \), but \( y = 1 \) and \( z = 1 \), so \( yz = 1 \), making \( F = 1 \).
- For the sixth row, \( x = 0 \), \( y = 1 \), but \( z = 0 \), so \( yz = 0 \), making \( F = 0 \).
- For the last two rows, \( x = 0 \), and either \( y = 0 \) or \( z = 0 \), making \( yz = 0 \), so \( F = 0 \).

Do you want further clarification on any steps? Here are five follow-up questions:

1. How would you represent the Boolean expression \( x + yz \) using logic gates?
2. What would the Karnaugh map look like for this Boolean function?
3. How would the result change if we modified the expression to \( x \cdot yz \)?
4. What is the dual of the Boolean function \( x + yz \)?
5. How can this truth table be simplified using Boolean algebra?

**Tip:** When dealing with truth tables, check each row step by step by focusing on how individual variables affect the overall output!

Complete the truth table for F(x, y, z) = x + yz

Learn how to complete the truth table for the Boolean expression F(x, y, z) = x + yz. This covers essential Boolean algebra concepts, logic gates, and truth tables. Suitable for high school students in Grades 9-12.

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