I am remodelling my kitchen,When i run the drain from the sink to the main drain, do i need to vent it? If i do have do i connect the vent above or after the p-trap? There is already a vent going outside, just need to know if the connection is after the trap or not. I also plan on installing an island dishwasher, i know it has to be vented out, but how would i do it, would i go through the floor back under the kitchen sink and connect to the existing vent thats there already? In regards to the drain from the dishwasher, would this be done the same as well or can i connect to the drain under the kitchen floor instead of coming back up under the sink?

Any help is appreciated

Thanks