Use truth tables to test the validity of the argument.
-$\begin{array} { l }
\mathrm { p } \sim \mathrm { q } \
\sim \mathrm { q }\
\hline\therefore \sim \mathrm { p }
\end{array}$

A) Valid
B) Invalid

Question

Use truth tables to test the validity of the argument.
-$\begin{array} { l } 
\mathrm { p } \sim \mathrm { q } \
 \sim \mathrm { q }\
\hline\therefore \sim \mathrm { p } 
\end{array}$

A) Valid
B) Invalid

Quizplus · Accepted Answer

The argument is valid because, in all cases where the premises are true, the conclusion is also true. The first premise states that $p$ implies $q$ ($p \rightarrow q$), and the second premise states that $q$ is false ($\sim q$). According to the rules of implication, if $q$ is false, then $p$ must also be false to maintain the truth of the first premise. Therefore, the conclusion that $p$ is false ($\sim p$) logically follows from the premises, making the argument valid.

Use Truth Tables to Test the Validity of the Argument p∼q∼q∴∼p\begin{array} { l } \mathrm { p } \sim \mathrm { q } \\ \sim \mathrm { q }\\\hline\therefore \sim \mathrm { p } \end{array}p∼q∼q∴∼p​​

Use Truth Tables to Test the Validity of the Argument $\begin{array} { l } \mathrm { p } \sim \mathrm { q } \\ \sim \mathrm { q }\\\hline\therefore \sim \mathrm { p } \end{array}$