Fsc Part 1 Mathematics (Complete Solution)

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Q4

Determine whether each of the following is a tautology, a contingency or an absurdity

**(i) p∧∼p**

Solution:

p | ∼p | p∧∼p |
---|---|---|

T | F | F |

F | T | F |

The last column shows that p→(q→p) is false for all values, so it is a absurdity.

**(ii) p→(q→p)**

Solution:

p | q | q→p | p→(q→p) |
---|---|---|---|

T | T | T | T |

T | F | T | T |

F | T | F | T |

F | F | T | T |

The last column shows that p→(q→p) is true for all values, so it is a tautology.

**(iii) q∨(∼q∨p)**

Solution:

p | q | ∼q | ∼q∨p | q∨(∼q∨p) |
---|---|---|---|---|

T | T | F | T | T |

T | F | T | T | T |

F | T | F | F | T |

F | F | T | T | T |

The last column shows that q∨(∼q∨p) is true for all values, so it is a tautology`.