# Construct a truth table for each of these compound propositions: i) (p ⇔ q) ⇔ (r ⇔ s) ii) (p ⨁ q) ∨ (p ⨁ ¬q)

## i. Truth Table for: (p ⇔ q) ⇔ (r ⇔ s)

p | q | r | s | p ⇔ q | r ⇔ s | (p ⇔ q) ⇔ (r ⇔ s) |
---|---|---|---|---|---|---|

T | T | T | T | T | T | T |

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

## ii. Truth Table for: (p ⨁ q) ∨ (p ⨁ ¬q)

p | q | ¬q | p ⨁ q | p ⨁ ¬q | (p ⨁ q) ∨ (p ⨁ ¬q) |
---|---|---|---|---|---|

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

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

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

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