# Determine which of the following pair of statement are logically equivalent: (r V p) ^ ( ( ~r V (p^q) ) ^ (r V q) ) and p ^ q

## Truth Table for: p → r q → r hence, p V q → r

p | q | r | ~r | p ^ q | ~r V (p^q) | r V q | r V p | (~r V (p^q)) ^ (r V q) | ((~r V (p^q) ) ^ (r V q)) ^ (r V p) |
---|---|---|---|---|---|---|---|---|---|

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

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

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

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

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

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

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

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

Since values in the column 5 and column 10 are same the give two statements are logically equivalent.