Fsc Part 1 Mathematics (Complete Solution)

Q4
AU(B∩C)=(AUB)∩(AUC)

Solution:

The corresponding formula of logic is

p ∨ (q ∧ r)=(p ∨ q) ∧ (p ∨ r)

we construct the truth table of the two sides

pqrp ∨ qq ∧ rp ∨ rp ∨ (q ∧ r)p ∨ (q ∧ r)=(p ∨ q) ∧ (p ∨ r)
T T T T T T T T
T T F T F T T T
T F T T F T T T
T F F T F T T T
F T T T T T T T
F T F T F F F F
F F T F F T 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) ∧ (p ∨ r)

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