I'm using counts of elements in sets, along with logic. So, for instance, I'd like to determine if
Count[$a \land \neg b$] = Count [$a$] - Count[$a \land b$]
Count[x] counts the total number of elements in a generic set. I don't want to really create the set $x$, I just want to be able to use the rules of logic alongside addition and subtraction of counts of elements of generic sets.
In general, I'd like to be able to use all of the rules of propositional logic. I'm really wondering, then, if there is some way to streamline the process of counting elements of sets. I've been doing the math by pencil and paper, and I sometimes run into problems with logic errors. Plus, it seems like this should be an easy problem for veteran Mathematica users. So can someone find an easy way to do this "set arithmetic" for generic sets?