Use a truth table to determine whether the argument is valid.
-$\begin{array} { c }
\sim \mathrm { p } \rightarrow \mathrm { q } \
\frac { \sim q \rightarrow p } { p \vee q }
\end{array}$
A) Valid
B) Invalid

Question

Use a truth table to determine whether the argument is valid.
-$\begin{array} { c } 
\sim \mathrm { p } \rightarrow \mathrm { q } \
\frac { \sim q \rightarrow p } { p \vee q }
\end{array}$
A) Valid
B) Invalid

Quizplus · Accepted Answer

The argument is valid because, for all cases where the premises are true, the conclusion is also true. In a truth table, if every instance where both premises $\sim p \rightarrow q$ and $\sim q \rightarrow p$ are true leads to $p \vee q$ being true, the argument is considered valid. This is the case here, as the premises ensure that either $p$ or $q$ (or both) must be true, which directly satisfies the conclusion $p \vee q$.

Use a Truth Table to Determine Whether the Argument Is ∼p→q∼q→pp∨q\begin{array} { c } \sim \mathrm { p } \rightarrow \mathrm { q } \\\frac { \sim q \rightarrow p } { p \vee q }\end{array}∼p→qp∨q∼q→p​​

Use a Truth Table to Determine Whether the Argument Is $\begin{array} { c } \sim \mathrm { p } \rightarrow \mathrm { q } \\\frac { \sim q \rightarrow p } { p \vee q }\end{array}$