This issue may be caused by a problem with the air admittance valve (AAV) or the vent pipe in the plumbing system. The AAV is a device that is installed in the drain line of the sink, which allows air into the system to equalize pressure and prevent water from flowing back into the sink when the toilet is flushed. If the AAV is faulty or improperly installed, it can cause the sink to run when the toilet is flushed.
The vent pipe also plays a role in preventing this issue, it allows air into the drain lines to balance the pressure, if the vent pipe is blocked, not properly installed or have any leaks it may cause the same problem. It's best to have a plumber inspect and diagnose the issue to determine the cause and provide a solution
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