#### Question

Prove that the following statement pattern is equivalent :

(p ∨ q) r and (p → r) ∧ (q → r)

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#### Solution

Truth table given is as follows:

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

p | q | r |
`A=p vv q` |
`B=p->r` |
`C=q->r` |
`A->r` |
`B ^^ C` |

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

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

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

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

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

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

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

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

Thus from column 7 and 8

(p ∨ q) r ≡(p → r) ∧ (q → r)

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Solution for question: Prove that the following statement pattern is equivalent : (p ∨ q) r and (p → r) ∧ (q → r) concept: Mathematical Logic - Statement Patterns and Logical Equivalence. For the courses HSC Arts, HSC Commerce, HSC Commerce (Marketing and Salesmanship), HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)