Fsc Part 1 Mathematics (Complete Solution)

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Q3

(A∩B)∩C=A∩(B∩C)

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 | F | F | F | F |

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

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

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

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

F | F | T | F | F | F | 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 ∧ r)