Fsc Part 1 Mathematics (Complete Solution)

#
Q2

(AUB)UC=AU(BUC)

Solution:

The corresponding formula of logic is

(p ∨q) ∨ r=p ∨ (q ∨ r)

we construct the truth table of the two sides

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

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

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

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

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

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

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

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

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 ∨ r)