Using the indirect method, construct a shortened truth table for the following argument and use it to determine whether the argument is valid or invalid. Explain exactly how your shortened truth table proves that the argument is valid or invalid. $($If need be$,$ your shortened truth table can be handwritten, photographed, and inserted into this response as an image. That said, if your shortened truth table is handwritten, it is your responsibility to make absolutely sure that $($a$)$ it is legible and $($b$)$ it is inserted as an image and not as a link to an image.$)$

$($P v Q$)$ ~ R $,$ ~ Q $/$ ~ P $$ R