Exercise 1.6 | Q 4.3 | Page 16

Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ (~p ∨ ~q)

p | q | ~p | ~q | p∧q | ~p∨~q | (p∧q)∧(~p∨~q) |

T | T | F | F | T | F | F |

T | F | F | T | F | T | F |

F | T | T | F | F | T | F |

F | F | T | T | F | T | F |

All the truth values in the last column are F. Hence, it is a contradiction.