# Solving systems of logial and set theoretic propositions

I need to allocate a couple of dozen elements into different sets, respecting some boundary conditions, and was hoping Mathematica might somehow help.

A simple example:

The propositions being

a) a $\in$(AvB)

b) b $\in$B

c) $\vert$$A\vert$=1

I would expect the answer to be: A={a}, B={b}.

Any hints? Thanks, indeed.

• What you've given us is a simple description of a simple example, not actually a simple example. Your description is great, but we need more Mathematica-specific details in the example. Please provide us with a simple example of what A, B, a, and b could be, in, say, List form. Or, is that you want Mathematica to logically deduce the result from the propositions? (In other words, are you asking Mathematica to do logical deductions, or are you asking it to sort elements into lists?) By the way, I think you need to add "d) a != b". – march Dec 9 '15 at 19:19
• @march Thanks for your comment! It is the latter: I want the program to logically deduce the result as it stands from exactly these propositions (plus the one you added). However, if there is another way around it, I would certainly appreciate to learn about it, too. In the end, I simply need to know which element has to be in which set such that all boundary conditions are met. – user3451767 Dec 9 '15 at 19:33
• All right, so maybe start here. (I've never used Mathematica for this, so I can't help. If it had been the former of my two guesses, I would've been able to help (most of us would have, actually).) – march Dec 9 '15 at 19:37