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The image shows a Boolean logic problem asking to complete a truth table for the Boolean function \( F = yz + z(xy)' \), where \( x \), \( y \), and \( z \) are the input variables. The inputs \( x \), \( y \), and \( z \) are listed in the table, and the truth table needs to be filled with the corresponding output values of \( F \).

Let’s evaluate the expression for each combination of \( x \), \( y \), and \( z \):

### Expression:
- \( F = yz + z(xy)' \)
- \( (xy)' \) is the negation of \( xy \), meaning it will be true when \( xy \) is false.

I will now calculate the output \( F \) for each row in the truth table.

### Truth Table:
- **Row 1:** \( x = 0 \), \( y = 0 \), \( z = 0 \)
- **Row 2:** \( x = 0 \), \( y = 0 \), \( z = 1 \)
- **Row 3:** \( x = 0 \), \( y = 1 \), \( z = 0 \)
- **Row 4:** \( x = 0 \), \( y = 1 \), \( z = 1 \)
- **Row 5:** \( x = 1 \), \( y = 0 \), \( z = 0 \)
- **Row 6:** \( x = 1 \), \( y = 0 \), \( z = 1 \)
- **Row 7:** \( x = 1 \), \( y = 1 \), \( z = 0 \)
- **Row 8:** \( x = 1 \), \( y = 1 \), \( z = 1 \)

Let me calculate the values for \( F \).It seems like I can’t do more advanced data analysis right now. Please try again later. Let me know if you want me to help with any other steps!

Complete the truth table given below for the Boolean function 'F' using the Boolean input variables x, y, and z with the binary values taken in the order given exactly in the table below as well:

x y z F = yz + z(xy)'
00 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

Enter 0 or 1 only as an answer in each blank going from left to right as they relate to the rows of the truth table when going from top to bottom.

Learn how to complete the truth table for the Boolean function F = yz + z(xy)' using the input variables x, y, and z. This problem covers key concepts in Boolean algebra and logic gates, making it suitable for high school students.

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