Fsc Part 1 Mathematics (Complete Solution)

#
Q2

Contruct truth tables for the following statements

**(i) (p→∼p)∨(p→q)**

Solution:

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

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

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

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

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

**(ii) (p∧∼p)→q**

Solution:

p | q | ∼p | p∧∼p | (p∧∼p)→q |
---|---|---|---|---|

T | T | F | F | T |

T | F | F | F | T |

F | T | T | F | T |

F | F | T | F | T |

**(iii) ∼(p→q)↔(p∧∼q)**

Solution:

p | q | ∼q | p→q | ∼(p→q) | p∧∼q | ∼(p→q)→(p∧∼q) | (p∧∼q)→∼(p→q) |
---|---|---|---|---|---|---|---|

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

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

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

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