Plumbers?

whats the minimum acceptable diameter for pipe for a toilet?

I want to put one upstairs, and will probably run 2 drains, one for a shower, and sink, the other for the toilet.

The only wall I can drop it through is a 2X4 wall, so is 2" ok?

also, should I add a vent for this, or is the one in the house acceptable?

Thanks in Advance :toothy4: