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Match List-I with List-II: List-IList-II (a) p→q (i) ¬(q→¬p) (b) p∨q (ii) p∧¬q (c) p∧q (iii) ¬p→q (d)…

Using \( p\to q\equiv\lnot p\lor q \): (a) \( p\to q \) matches (iv) \( \lnot p\lor q \); (b) \( p\lor q\equiv\lnot p\to q \), matching (iii); (c) \( \lnot(q\to\lnot…

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Match List-I with List-II:

List-IList-II
(a) p→q(i) ¬(q→¬p)
(b) p∨q(ii) p∧¬q
(c) p∧q(iii) ¬p→q
(d) ¬(p→q)(iv) ¬p∨q
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Answer and explanation

Correct answer D

Using p→q≡¬p∨q p\to q\equiv\lnot p\lor q : (a) p→q p\to q matches (iv) ¬p∨q \lnot p\lor q ; (b) p∨q≡¬p→q p\lor q\equiv\lnot p\to q , matching (iii); (c) ¬(q→¬p)≡¬(¬q∨¬p)≡p∧q \lnot(q\to\lnot p)\equiv\lnot(\lnot q\lor\lnot p)\equiv p\land q , matching (i); and (d) ¬(p→q)≡p∧¬q \lnot(p\to q)\equiv p\land\lnot q , matching (ii). Pairing p∨q p\lor q with ¬(q→¬p) \lnot(q\to\lnot p) is wrong because that expression reduces to a conjunction, not a disjunction.

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  • UGC NET Computer Science and Applications

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