Q56.Marks: +2.0UGC NET Paper 2: Computer Sc 23rd August 2024 Shift 1
Consider the following if p and q are two statements.
(A) ~(p∧q) ≡ ~p∨~q
(B) ~(p∨q) ≡ ~p∧~q
(C) p∧~p ≡ T
(D) (p ⇒ q) ≡ p∧~q
(E) p∨q ≡ ~p∨~q
Choose the correct answer from the options given below :
1.(A), (B) and (D) Only
2.(A), (C) and (D) Only
3.(C), (D) and (E) Only
4.(A), (B) only✓ Correct
Solution
The correct answer is Option 4) (A), (B) only
Key Points
(A) ~(p∧q) ≡ ~p∨~q
✔️ This is De Morgan’s Law and is logically correct. The negation of a conjunction is equivalent to the disjunction of the negations.
(B) ~(p∨q) ≡ ~p∧~q
✔️ This is also De Morgan’s Law. The negation of a disjunction is equivalent to the conjunction of the negations.
(C) p∧~p ≡ T
❌ Incorrect. This is a contradiction. p∧~p is always false, so it should be equivalent to F (False), not T (True).
(D) (p ⇒ q) ≡ p∧~q
❌ Incorrect. The implication (p ⇒ q) is logically equivalent to ~p ∨ q, not p∧~q. In fact, p∧~q represents the condition under which p ⇒ q is false.
(E) p∨q ≡ ~p∨~q
❌ Incorrect. This is not a valid logical equivalence. p∨q is not equivalent to ~p∨~q. In fact, these are generally not logically equivalent.
Correct Logical Equivalences:
(A) and (B) – Valid De Morgan’s Laws.
(C) – Invalid, as it expresses a contradiction being True, which is false.
(D) – Invalid equivalence for implication.
(E) – Invalid, not a standard equivalence.
Therefore, the correct answer is: Option 4) (A), (B) only
