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Per the installation instructions for the Liberty 404 Sink/Drain Pump System:
Provision is made for a vent stack to allow extra volume for high suds conditions, and to ensure proper drainage of the fixture. HAND-TIGHTEN ONLY. DO NOT CAP-OFF VENT. DO NOT use ONE-WAY QUICK-VENTS or AIR ADMITTENCE VALVES as they will not guarantee proper fixture performance. The vent pipe should have a union to facilitate removal if required and shall be connected directly to a building or house vent.
This is pretty standard for all of these systems.