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.”
- $p \wedge q \rightarrow \neg r$
- $p \rightarrow q$
- $\neg (p \wedge \neg q)$
Which of the following is/are correct Formulation of the above sentence?
- $\text{X-1, Y-3, Z-2}$
- $\text{X-2, Y-1, Z-3}$
- $\text{X-1, Y-2, Z-3}$
- $\text{X-3, Y-2, Z-1}$