a 12-slice

P: Pepperoni

M: Mushroom

U: one or the other or both

∩: Both at the same time

P U M = 12       P = 5      M = 8

A formula (that I got from probability theory) says that:

A ∩ B = A + B - A U B 

In our case:

P ∩ M = P + M - P U M = 5 + 8 - 12 = 1 

So the pizza consists of 4 slices w/ only pepperoni, 7 slices w/ only mushroom, and 1 slice w/ both. 

Darn, it took me at least 5 min to find out how to solve this... :)

But the important thing, Tetration,  is that you did.....!!!!!

Yeah, I know :)