The majority of my basement is finished and I am finally getting around to finishing the small kitchen area. When the original work was completed, the plumber set it up for an under counter sump pump. I have attached a picture of the sink outlet (on the left), and the vent and outlet to the sewer (right side of the corner). My question is, how can I tell which of the outlet pipes on the right side is the vent and which is linked to the overhead sewer, without cutting away the drywall?
Those should have been labelled. Bad Plumber. Or possibly bad painter, if it was written on the wall by the plumber.
With a squirt bottle or water-balloon, perhaps. Or a hose.
Put water into each pipe. If the vent does not have a downward leg behind the wall, water would come back out of it, and water should not come back out of the drain line.
If they both take water and don't spit it back at you, time to cut some drywall (it's under a counter, so repairing it should not be a big deal.)
You could also try a cell-phone or pad camera (with flash/light) shooting straight into the pipes, and see if it looks like one turns up and the other down within sight. You might be able to do that with a flashlight, but it's easier to get light and vision at the same time with the techno-toys - if the camera will focus, anyway.