Let p and q be distinct prime formulas (a.k.a. atomic propositions) and P be a set constructed as follows: 1) p and q are in P; 2) if r and s are in P, then (r -> s) is in P. Prove that no formula in P is tautologically equivalent to (p & q). In other words, there exists no t in P such that tv = T when pv = T and qv = T; = F otherwise. I can't get anywhere. I'll be going through the possibilities until I notice something. Oh, nevermind, I got it by contradiction and going backwards; every possibility dead ends. Maybe there's a better (more useful) way though.