Question $5(10$ points$)$

Is the following argument valid? Construct a full truth table in order to test its yalidity: label which columns are premises, which column is the conclusion, which rows are critical rows, and how that proves the argument is $($in$)$valid$.$

If it's cold or raining, then we're not going hiking.

It's not cold and we're going hiking.

Therefore, it's not raining.

$\backslash$table$[[p,q,r,],[$T$,$T T$,$T$,],[$T$,$T$,$F$,],[$T$,$F$,$T$,],[$T$,$F$,$F$,],[$F$,$T$,$T$,],[$F$,$T$,$F$,],[$F$,$F$,$T$,],[$F$,$F$,$F$,]]$

$($Same as before, this table is not interactable but can serve as a template$)$