Using the rules of negation, write the negation of the following: (~p ∧ q) ∧ (~q ∨ ~r)

EXERCISE 1.8Q 2.3   PAGE 21
Exercise 1.8 | Q 2.3 | Page 21

Using the rules of negation, write the negation of the following:

(~p ∧ q) ∧ (~q ∨ ~r)


SOLUTION

~[(~p ∧ q) ∧ (~q ∨ ~r)]

≡ ~(~ p ∧ q) ∨ ~ (~ q ∨ ~r)    ...[Negation of conjunction]

≡ [~(~ p) ∨ ~ q] ∨ [~(~q) ∧ ~(~r)]  ...[Negation of conjunction and disjunction]

≡ (p ∨ ~q) ∨ (q ∨ r)      .....[Negation on negation]