Let p and q be distinct prime formulas (a.k.a. atomic propositions) and P be a set constructed as follows:(adsbygoogle = window.adsbygoogle || []).push({});

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 t^{v}

= T when p^{v}= T and q^{v}= 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.

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# Logic; prove set of connectives incomplete

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