JAMIA 2022 — Mathematics PYQ
JAMIA | Mathematics | 2022Negation of q v ~ (p ^ r) is
Choose the correct answer:
- A. q ~ ^ ~ (p ^ r )
- B. ~q ^ (p ^ r)(Correct Answer)
- C. ~ q v (p ^ r)
- D. ~ q v ~ (p ^ r)
~q ^ (p ^ r)
Explanation
1. Set Up the Negation
We want to find the result of applying the negation operator (¬) to the entire expression:
¬[q∨¬(p∧r)]
2. Apply De Morgan’s Law (First Step)
De Morgan's Law states that ¬(A∨B)≡¬A∧¬B.
Applying this to our expression:
¬q∧¬[¬(p∧r)]
3. Apply the Double Negation Law
The Law of Double Negation states that ¬(¬A)≡A.
Applying this to the second part of our expression:
¬q∧(p∧r)
4. Final Simplified Form
By removing the unnecessary brackets, the final expression is:
¬q∧p∧r
Explanation
1. Set Up the Negation
We want to find the result of applying the negation operator (¬) to the entire expression:
¬[q∨¬(p∧r)]
2. Apply De Morgan’s Law (First Step)
De Morgan's Law states that ¬(A∨B)≡¬A∧¬B.
Applying this to our expression:
¬q∧¬[¬(p∧r)]
3. Apply the Double Negation Law
The Law of Double Negation states that ¬(¬A)≡A.
Applying this to the second part of our expression:
¬q∧(p∧r)
4. Final Simplified Form
By removing the unnecessary brackets, the final expression is:
¬q∧p∧r