Use truth tables to test for the validity of these two argument forms.  (Remember that you need eight lines since there are three letters in use.)

1.  (P & Q) -> R,  ~R  |- ~P
P
 Q R (P & Q) -> R ~R
 ~P
1
 1
 1
         1
 0
 0
1
 1
 0
         0
 1
 0
1
 0
 1
        1
 0
 0
1
 0
 0
        1
 1
 0
0
 1
 1
        1
 0
 1
0
 1
 0
        1
 1
 1
0
 0
 1
        1
 0
 1
0
 0
 0
        1
 1
 1
Invalid   (you have a bad line when P is true but both Q and R are false)


2.  (P v Q) -> R,  ~R  |-  ~P
P
 Q
 R
 (P v Q) -> R
 ~R
 ~P
1
 1
 1
        1
 0
 0
1
 1
 0
        0
 1
 0
1
 0
 1
        1
 0
 0
1
 0
 0
          0 
1
 0
0
 1
 1
       1
 0
 1
0
 1
 0
       0
 1
 1
0
 0
 1
       1
 0
 1
0
 0
 0
       1
 1
 1
valid (there are no bad lines)