Exercise 1.7 (1)

1. Write the dual of each of the following :

i) (p ∨ q) ∨ r
Ans: (p ∧ q) ∧ r

ii) ∼ (p ∨ q) ∧ [p ∨ ∼ (q ∧ ∼ r)]
Ans: ~ (p ∧ q) ∨ [p ∧ ~q ∨ ~ r)]

iii) p ∨ (q ∨ r) ≡ (p ∨ q) ∨ r
Ans: p ∧ (q ∧ r) ≡ (p ∧ q) ∧ r

iv) ∼ (p ∧ q) ≡ ∼ p ∨ ∼ q
Ans: ∼ (p ∨ q) ≡ ∼ p ∧ ∼ q