retagged by
753 views
3 votes
3 votes

Let’s consider a propositional language where

  • $p$ means “Paola is happy”,
  • $q$ means “Paola paints a picture”,
  • $r$ means “Renzo is happy”.

Consider the following sentences and propositional logic formulas :

  • $\text{X} :$ “if Paola is happy and paints a picture, then Renzo isn’t happy.”
  • $\text{Y} :$ “if Paola is happy, then she paints a picture.”
  • $\text{Z} :$ “Paola is happy only if she paints a picture.”
  1. $p \wedge q \rightarrow \neg r$
  2. $p \rightarrow q$
  3. $\neg (p \wedge \neg q)$

Which of the following is/are correct Formulation of the above sentence?

  1. $\text{X-1, Y-3, Z-2}$
  2. $\text{X-2, Y-1, Z-3}$
  3. $\text{X-1, Y-2, Z-3}$
  4. $\text{X-3, Y-2, Z-1}$
retagged by

1 Answer

3 votes
3 votes

$\neg (p \wedge \neg q)$  is equivalent to $p \rightarrow q$.

So, Option A; C are correct.

Detailed Video Solution:

https://youtu.be/nclBhBmtz2g?t=5893

edited by
Answer:

Related questions

5 votes
5 votes
1 answer
1
GO Classes asked Mar 30, 2022
672 views
Consider the following atomic propositions:$\text{R}$: It is Raining$\text{S}$: Sonu is SickWhich of the following is/are correct English Translation of the following log...