Fsc Part 1 Mathematics (Complete Solution)

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Q1

Convert the following theorems to logical form and prove them by constructing truth tables

**1. (A∩B)'=A'U B'**

SOLUTION:The corresponding formula of logic is

∼(X∧y)=∼X ∨ ∼Y

We constuct truth table of the two sides

X | Y | ∼X | ∼Y | X∧Y | ∼(X∧Y) | ∼X ∨ ∼Y | ∼(X∧Y)=∼X ∨ ∼Y |
---|---|---|---|---|---|---|---|

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

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

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

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

The last two columns of the table establish the equality of the two sides of ∼(X∧Y)=∼X v ∼Y