Tip:A–D to answerE for explanationV for videoS to reveal answer
The negation of the statement (p∨q)∧(q∨(∼r)) is:
- A.
((∼p)∨r)∧(∼q)
(Correct Answer) - B.
((∼p)∨(∼q))∧(∼r)
Correct Answer: ((∼p)∨r)∧(∼q)
Explanation
-
Apply De Morgan's Law: ∼[(p∨q)∧(q∨(∼r))]=[∼(p∨q)]∨[∼(q∨(∼r))].
-
Simplify further: [(∼p)∧(∼q)]∨[(∼q)∧r].
-
Apply Distributive Law: (∼q)∧[(∼p)∨r].
Explanation
-
Apply De Morgan's Law: ∼[(p∨q)∧(q∨(∼r))]=[∼(p∨q)]∨[∼(q∨(∼r))].
-
Simplify further: [(∼p)∧(∼q)]∨[(∼q)∧r].
-
Apply Distributive Law: (∼q)∧[(∼p)∨r].
