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GATE CSE 2017 Set 1 | Question: 01

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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
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8 Answers

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Answer is (D)

The main Concept is Contrapositive.

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

Q ------>P <=> ~P -------->~Q (Converge = Inverse)
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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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Easy.

p’ → q’ = p + q’

Simplify all the options, we’ll get p+q’ for option II and III
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