Exercise 1.6 | Q 7.3 | Page 16

Prove that the following pair of statement pattern is equivalent.

p → q and ~ q → ~ p and ~ p ∨ q

1 | 2 | 3 | 4 | 5 | 6 | 7 |

p | q | ~p | ~q | p→q | ~q→~p | ~p∨q |

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

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

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

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

In the above table, entries in columns 5, 6 and 7 are identical.

∴ Statement p → q and ~q → ~p and ~p ∨ q are equivalent.