Is this sink plumbed correctly?

[KeithMyers]

This is a double sink located in my kitchen. It appears to have a vent installed as well as an open vertical pipe after a P trap that doesn't seem to have a purpose. On occasion my wife and I get a whiff of a sewage smell and it almost always stinks underneath the cabinet. I am not a plumber but know a few basics. This just doesn't seem right and was looking for some help.

The vertical pipe in the right of the picture terminates directly below the sink and is open on the end.

Thanks in advanced for the help,

Keith

 

[frodo]

do you want the quick fix or the right fix?

quick fix, cut the pipe add cap

to do it right, remove that wye that i have a blue arrow pointed at, and replumb the drain

 

[KeithMyers]

Thanks for your help I will probably cap it where you mentioned frodo. Any idea why it was plumbed in this way?

 

[frodo]

the code reads you must have an air gap on the dishwasher, most likely, the hose was connected to the stand pipe in lieu of a air gap fitting,
then was hooked to the disposal because of splashing,

you can cut and cap. BUT, be aware, food will back up into that part of the wye, a little at a time, sooner or later. your drain will glog up
and you can find the problem there.

so, here is the real deal.... do you fix it now, when everything is dry and clean.
or
do you wait till the sink backs up, and its a total mess to deal with. choice is yours,