Miscellaneous Exercise 1 | Q 4.13 | Page 33

Determine whether the following statement pattern is a tautology, contradiction, or contingency.

[~(p ∨ q) → p] ↔ [(~p) ∧ (~q)]

p | q | ~p | ~q | p∨q | ~(p∨q) | ~(p∨q)→p | (~p)∧(~q) | [~(p∨q)→p]↔[(~p)∧(~q)] |

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

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

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

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

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