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

pqrp ∨ qq ∨ r(p ∨ q) ∨ rp ∨ (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)

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