Great question — answering as the UphillTech team:
You show a trap for the laundry, so you need a trap for both sinks and the shower, if you don't fit them then you could / will end up with smells coming in...
Full answer by Solar Mike: https://diy.stackexchange.com/a/161889 (CC BY-SA 4.0).
Need it done for your business? UphillTech.