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Let p,q and r be three propositions. Prove or disapprove $(p\to q) \land (q \iff r) \land (p \lor \lnot (\lnot q \lor \lnot r) \equiv p \land q \land r$

so, the way i do is LHS = $(\lnot p\lor q) \land (\lnot q \lor r) \land (\lnot r \lor q) \land (p \lor q) \land (p \lor r)$

so what should I do next? Or am I completely wrong?

LeonBrain
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  • I suppose you could use the method of analytic tableaux to give you some ideas, but that's somewhat indirect. I can't think of much else. – Shaun Nov 18 '13 at 10:16

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The statement is false. Suppose q and r are true but p is false. The left side will be true and the right side will be false.

Geoff Naylor
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  • Is the only way to solve this question using truth table?? – LeonBrain Nov 18 '13 at 10:45
  • Well for disproving logical formulae usually you find an interpretation of the atomic sentences (that is assigning them true or false) that makes it false. To prove it you usually use rules of inference. A truth table works too but it's quite brutish as the number of interpretations of atoms exponentially increases with the number of them – Geoff Naylor Nov 25 '13 at 11:51