On the Subject of Logic Plumbing

All of the valves have been replaced with gates!

On the module is a 6x6 grid of logic gates. Each tile takes inputs from the current state of the tiles (or lights) above and to the left, and performs the operation on the tile to evaluate its state.

To solve the module, each tile must evaluate to “true” if the tile is yellow, and “false” if the tile is white. You may swap the gates on two tiles by pressing them in sequence. Additionally, you may check what every tile evaluates to at any time by holding the button at the top left. A green tile indicates that the current state matches the desired state, not whether the current state is true or false.

This module cannot strike you. Hold the button at the top left to solve the module when all tiles evaluate to the right state.

X ∧ Y
X ∨ Y
X ⊻ Y
X | Y
X ↓ Y
X ↔ Y