Fsc Part 1 Mathematics (Complete Solution)

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Q4

AU(B∩C)=(AUB)∩(AUC)

Solution:

The corresponding formula of logic is

p ∨ (q ∧ r)=(p ∨ q) ∧ (p ∨ r)

we construct the truth table of the two sides

p | q | r | p ∨ q | q ∧ r | p ∨ r | p ∨ (q ∧ r) | p ∨ (q ∧ r)=(p ∨ q) ∧ (p ∨ r) |
---|---|---|---|---|---|---|---|

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

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

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

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

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

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

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

F | F | F | F | F | F | F | F |

The last two columns of the table establish the equality of the two sides of p ∨ (q ∧ r)=(p ∨ q) ∧ (p ∨ r)