Fsc Part 1 Mathematics (Complete Solution)

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

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 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)

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