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GATE CSE 2017 | Set 1 | Question: 01

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45 45 votes

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. $\left ( ¬p \right ) \vee q$
  1. I only
  2. I and IV only
  3. II only
  4. II and III only

8 Answers

Best answer
44 44 votes
$(\neg P\to \neg Q)$ 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).
• edited by
12 12 votes
Given statement : ~p $\Rightarrow$ ~q

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

= p $\vee$ ~q

= ~q $\vee$ p

= q $\Rightarrow$ p

$\therefore$ D should be answer.
4 4 votes

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

4 4 votes

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

4 4 votes
Answer is (D)

The main Concept is Contrapositive.

 P------>Q <=> ~Q --------> ~P (Implication =Contrapositive)

Q ------>P <=> ~P -------->~Q (Converge = Inverse)
0 0 votes
option D, as 2 and 3 are Equvalent . and 1 is false and 1 and 4 are same so if 1 is false then both 1, 4 will false hence D
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