List-I	List-II
(a) $p \to q$	(i) $\neg(q \to \neg p)$
(b) $p \vee q$	(ii) $p \wedge \neg q$
(c) $p \wedge q$	(iii) $\neg p \to q$
(d) $\neg(p \to q)$	(iv) $\neg p \vee q$

Choose the correct option from those given below:

First,

$p \to q \equiv \neg p \vee q$

So,

$(a) \rightarrow (iv)$

Now,

$\neg p \to q \equiv p \vee q$

So,

$(b) \rightarrow (iii)$

Now,

$q \to \neg p \equiv \neg q \vee \neg p$

Therefore,

$\neg(q \to \neg p)=\neg(\neg q \vee \neg p)$

Using De Morgan’s law,

$\neg(\neg q \vee \neg p)=q \wedge p$

$=p \wedge q$

So,

$(c) \rightarrow (i)$

Now,

$\neg(p \to q)=\neg(\neg p \vee q)$

Using De Morgan’s law,

$\neg(\neg p \vee q)=p \wedge \neg q$

So,

$(d) \rightarrow (ii)$

Therefore, the correct matching is

$(a)-(iv);\ (b)-(iii);\ (c)-(i);\ (d)-(ii)$