Examples Sheet: short truth-tables Test the following argument forms for validity by the short truth-table method. i) Q, P ↔ Q├ P ii) Q → R├ (P v Q) → (P v R) iii) (P & Q) → R , P→ R├ Q → R iv) P → Q , R → S├ (P v R) → (Q v S) v) (P & Q) → R├ ((P & Q) → R) v ((Q & ~P) → R) vi) P → Q , R → S , P v R├ Q & S vii) P ↔ Q , Q → R , ~R v S , ~P v S├ S viii) (S → P) & (T → R) , S v T, S → ~R , T→ ~P ├ R ↔~P ix) (Q & R) → S , (S & T) → P , ~U → (T & ~P) ├ (Q & R) → U x) S v T , Q→ ~(P v U) , R → ~(W & V) , (~V & T) & P ├ Q xi) P → (Q & R) , S ↔ (Q & T) , Q → (~P v S)├ ~R → T
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