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1. (P^Q)(PQ)
P | Q | (P^Q) | (PQ) | (P^Q)(PQ) |
V | V | V | V | V |
V | F | F | V | V |
F | V | F | V | V |
F | F | F | F | V |

2. (P^Q)(Q^R)}
P| Q | R | (P^Q) | (Q^R) | (P^Q)(Q^R) | (P^Q)(Q^R)} |
V | V | V | V | V | V | F |
V | V | F | F | F | V | F |
V | F | V | F | F | V | F |
V | F | F | F | F | V | F |
F | V | V | F | V | F |V |
F | V | F | F | F | V | F |
F | F | V | F | F | V | F |
F | F | F | F | F | V | F |

3.- (PQ)^(PQ)}

P | Q | (PQ) | (PQ) | (PQ)^(PQ) | (PQ)^(PQ)} |
V | V | V | V | V | F |
V | F |V | F | F | V |
F | V | V | V | V | F |
F | F | F | V | F | V |

4.- P^(QR)(PR)
P | Q | R | (QvR) |   (P^(QvR) | R | (PR) | (PR) | (P(QR)(PR) |
V | V | F | V | V | V | V | F | F |V | V | V | V | V | F | V | F | F |
V | F | F | F | F | V | V | F | V |
V | F | V | V | V | F | V | F | F |
F | V | F | V | F | V | V | F | V |
F | V | V | V | F | F | F | V | F |
F | F |F | F | F | V | V | F | V |
F | F | V | V | F | F | F | V | F |

5.- ((P^Q)^R)^(PR)
P | Q | R | (P^Q) | (P^Q)^R) | ~P | ~R | (~Pv~R) | ((P^Q)^R)^(~Pv~R) |
V | V | F | V | V | F | V | V | V |V | V | V | V | V | F | F | F | F |
V | F | F | F | F | F | V | V | F |
V | F | V | V | V | F | F | F | F |
F | V | F | F | F | V | V | V | F |
F | V | V | F | V | V | F | V | V |
F | F |F | F | F | V | V | V | F |
F | F | V | F | V | V | F | V | V |