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Logic

Prove: ~(R&T)
(p1) ~(P&Q)
(p2) (~P v ~Q) -> (~R v ~T)

~(~PV~Q)V(~RV~T) by defn of conditional
(P&Q)V(~RV~T)
(~RV~T) since (P&Q) is a contradiction of p1
~(R&T)

Nice. I was thinking along these lines:

~(P&Q) -> ~(R&T) by DMT

By the way, all of this logic... are you guys doing this for philosophy, or engineering?
 
This is probably the smartest thread I've seen on TB in a long time.

Just to dumb it down a bit, where would you actually use these logic problems in real life or a professional setting?

In computer programming for sure, syntax is different (different languages have different syntax anyway), but logic is logic with computer programming.. you can also assign the variables to actual sentences/statements to prove conclusions or even to derive whether or not certain statements are valid.

Also, in logic, we studied truth tables, deductive/inductive reasoning, identifying fallacies (really cool), and translating english into logical languages.. :)