Convert the compound statement into words.
-$$\begin{array} { l }
\mathrm { p } = \text { "Students are happy." } \
\mathrm { q } = \text { "Teachers are happy." } \
\sim \left( \mathrm { p } _ { \vee } \sim \mathrm { q } \right)
\end{array}$$
A) It is not the case that students are happy and teachers are not happy.
B) It is not the case that students are happy or teachers are not happy.
C) Students are not happy or teachers are not happy.
D) Students are not happy and teachers are not happy.

Question

Convert the compound statement into words.
-$$\begin{array} { l } 
\mathrm { p } = \text { "Students are happy." } \
\mathrm { q } = \text { "Teachers are happy." } \
\sim \left( \mathrm { p } _ { \vee } \sim \mathrm { q } \right)
\end{array}$$
A) It is not the case that students are happy and teachers are not happy.
B) It is not the case that students are happy or teachers are not happy.
C) Students are not happy or teachers are not happy.
D) Students are not happy and teachers are not happy.

Quizplus · Accepted Answer

The given statement is the negation of a disjunction, where $p$ is "Students are happy" and $\sim q$ is "Teachers are not happy." Thus, it translates to "It is not the case that students are happy or teachers are not happy."

Convert the Compound Statement into Words A) It Is Not the Case That Students Are Happy