GATE CSE 2017 Set 1 | Question: 01

Question

The statement $\left ( ¬p \right ) \Rightarrow \left ( ¬q \right )$ is logically equivalent to which of the statements below?

1. $p \Rightarrow q$
2. $q \Rightarrow p$
3. $\left ( ¬q \right ) \vee p$
4. $\left ( ¬p \right ) \vee q$

• A. I only
• B. I and IV only
• C. II only
• D. II and III only

Answer 1

$(\neg P\to \neg Q)$ can also be written as $(P \vee \neg Q),$ so statement $3$ is correct.

Now taking the contrapositive of $(\neg P\to \neg Q)$, we get $(Q\to P)$ hence statement $2$ is correct.

So, the answer is OPTION (D).

Comments

i also think the same...

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Ref:

Answer 2

Given statement : ~p $\Rightarrow$ ~q

= ~(~p) $\vee$ ~q

= p $\vee$ ~q

= ~q $\vee$ p

= q $\Rightarrow$ p

$\therefore$ D should be answer.

Answer 3

Option D.

$(\sim p) \Rightarrow (\sim q)$

$\sim (\sim p) \vee (\sim q)$

$p \vee (\sim q)$

$ (\sim q) \vee p$ ----------------> III is True

$q \Rightarrow p$   -----------------> II is True

Answer 4

we know that p→ q   is equivalent to ~p v q

similarly ~p→~q will be equivalent to p v ~q (III)

and implication is equivalent to contrapositive ,  ~p→~q   will be equivalent to q→ p (II)

answer: Both II & III ,OPTION D