Adding Washer/Water Heater Drain

I am in the process of buying my mother a house in Idaho. The bathroom has a washer with no drain and a water heater closet with no drain.
I attempted to hand draw the layout of the room.
The house is on a slab built at least 30-40 years ago which makes everything harder.
Previously the washer was drained into the tub/toilet and the W/H had no drain for the pressure relief valve.
I need to find a way to add drains for both the washer and the W/H. Can I connect them to the 2in vent that is on the exterior wall?
What would the proper layout be?
The Vent pipe is on the exterior of the wall...

I forgot to mention, the 2in vent is only connected to the toilet line.

You cannot connect them to the vent. You will need to cut the slab to join the line in the floor. The vent for the laundry may tie into the existing vent.

In addition, the washer must be a 2" drain and the standpipe must be trapped.

Air = vent pipe
Water = waste pipe

Question: Can water go down the air pipe?

I'm still thinking.................

I don't think so.
If you can find a water pipe, that would work.

I am not a plumber!

I don't claim to be a plumber.

I am trying to get my head around this problem so that when we contract this out I know what I should expect.

"Air & Water†I know the difference in theory but not application, remember I am not a plumber...

When I look at diagrams I notice many that show the "Main Stack" with many ancillary connections and it ultimately vents out of the roof, so pardon my ignorance and please just help me!

Playful comments are fine and I understand jerking around with the new guy but please don't just be rude...

Here is a washer rough-in.
Does the water heater need a drain for the relief only, or does it need a floor drain?

Obama the Plumber said:

Here is a washer rough-in.
Does the water heater need a drain for the relief only, or does it need a floor drain?

Click to expand...

The pressure relief valve needs a drain only.

In that picture, it looks like the same pipe is used to vent and drain, so there-in lies my confusion.

That is a great picture bt the way!

If you look at the washer p-trap and follow it to the left, you will see a wye fitting for the vent,
Go a bit farther left, and you see a laundry tray (sink) drain above the tee, that is vented out the top of the tee.

The "washer" air vent, since it is horizontal, needs a wye.

The "sink" fitting to air vent, can be a tee (santee) since it is vertical.

Both air vents, "washer vent" and "sink vent" tie together above the "flood" level of both plumbing fixtures.

Flood level means, the washer and the sink would overflow onto the floor before it got as high as the top tee.
This way, backed up waste can not rise so high as to go up and over to the other plumbing fixture. The water floods onto the floor first.

Look lower, the washer connects "below" the sink drain.
The pipe going down is "water" waste.