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GO Classes DPP | GATE CS | Discrete Mathematics| Propositional Logic

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4 4 votes

Let $p$ : "Jupiter is a planet" and $q$ : "India is an island." Which of the following is the correct verbal description of $p \rightarrow \neg q$ ?

  1. Jupiter is a planet if and only if India is not an island
  2. If India is not an island then Jupiter is a planet
  3. Jupiter is not a planet or India is not an island
  4. If Jupiter is a planet then India is not an island

5 Answers

2 2 votes

$$p \rightarrow \sim q$$

                                                    $\equiv$ If Jupiter is a planet then India is not an island.

 

Conclusion

$$\therefore (D)$$                                                                                                            is true

• edited by
1 1 vote

p: Jupiter is a planet

q: India is an island

¬q: India is not an island

p → ¬q: If Jupiter is a planet then India is not an island

 

Answer: D

0 0 votes

Given -

p -> ~q

Matching options -

C and D only

p -> ~ q is equivalent to ~p V ~q 

Option D is direct interpretation (As correct verbal description is asked)

• edited by
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