The vent under the sink is called a studor vent.It is like a check valve, it lets air into the sanitary drain and then closes so no gases can enter the room.They work very well and sometimes safer than a vent through the roof as air only enters the studor vent. A s-trap is not on the shower they are N/A.You have a p-trap just like under the sink but glued PVC. Most likely 2" pvc.
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