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
Negation of (p∨q)(q∨(∼r))
=∼[(p∨q)∧(q∨(∼r))]
=∼(p∨q)∨∼(q∨(∼r))
=((∼p)∧(∼q))∨((∼q)∧r)
=(∼p∧∼q)∨(r∧∼q)
=((∼p)∨r)∧(∼q)
Explanation
Negation of (p∨q)(q∨(∼r))
=∼[(p∨q)∧(q∨(∼r))]
=∼(p∨q)∨∼(q∨(∼r))
=((∼p)∧(∼q))∨((∼q)∧r)
=(∼p∧∼q)∨(r∧∼q)
=((∼p)∨r)∧(∼q)
