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

q ∨ [~ (p ∧ q)]

#### SOLUTION

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

T | T | T | F | T |

T | F | F | T | T |

F | T | F | T | T |

F | F | F | T | T |

All the truth values in the last column are T. Hence, it is a tautology.