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Match the following : List - IList - II (a) (p→q)⇔(¬q→¬p) (i) Contrapositive (b) [(p∧q)→r]⇔[p→(q→r)]…

\((p\to q)\Leftrightarrow(\neg q\to\neg p)\) is the contrapositive law (i); \([(p\wedge q)\to r]\Leftrightarrow[p\to(q\to r)]\) is the exportation law (ii); \((p\to…

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Match the following :

List - IList - II
(a) (p→q)⇔(¬q→¬p)(i) Contrapositive
(b) [(p∧q)→r]⇔[p→(q→r)](ii) Exportation law
(c) (p→q)⇔[(p∧¬q)→o](iii) Reductio ad absurdum
(d) (p↔q)⇔[(p→q)∧(q→p)](iv) Equivalence

Codes : (a), (b), (c), (d)

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Answer and explanation

Correct answer A

(p→q)⇔(¬q→¬p)(p\to q)\Leftrightarrow(\neg q\to\neg p) is the contrapositive law (i); [(p∧q)→r]⇔[p→(q→r)][(p\wedge q)\to r]\Leftrightarrow[p\to(q\to r)] is the exportation law (ii); (p→q)⇔[(p∧¬q)→o](p\to q)\Leftrightarrow[(p\wedge\neg q)\to o], where o is a contradiction, is reductio ad absurdum (iii), since assuming p and not-q leads to falsity; and (p↔q)⇔[(p→q)∧(q→p)](p\leftrightarrow q)\Leftrightarrow[(p\to q)\wedge(q\to p)] defines equivalence (iv). The code is (i), (ii), (iii), (iv).

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