Fsc Part 1 Mathematics (Complete Solution)

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

XY∼X∼YX∧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

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