To determine the output function \( F \) from the given logic circuit, we will analyze each gate step-by-step.

Identify the Gates: The circuit consists of NOT gates, AND gates, and an OR gate.

Analyze the Input and Output of Each Gate:

• The inputs \( X \) and \( Y \) are given.
• The NOT gate inverts \( X \) to give \( \overline{X} \). Similarly, it inverts \( Y \) to give \( \overline{Y} \).
• An AND gate receives inputs \( X \) and \( Y \) and provides \( XY \) as output.
• The NOT gate after the AND gate inverts \( XY \) to yield \( \overline{XY} \).
• Another AND gate receives inputs \( X \) and \( \overline{Y} \) and outputs \( X\overline{Y} \).

Combine Using the OR Gate:

The OR gate combines the outputs: \( \overline{XY} \), \( \overline{X} \), and \( X\overline{Y} \). So, the output function \( F \) is:

\(\overline{XY} + \overline{X} + X\overline{Y}\)

Conclusion: The correct options for the output function \( F \) based on the analysis are:

• \(\overline{XY}\)
• \(\overline{X} + \overline{Y} + X\overline{Y}\)
• \(\overline{XY} + \overline{X} + X\overline{Y}\)