Use the reverse method to test the following argument forms for validity.

1.  P -> (Q v R), S -> P, S & ~Q |- R

P Q R S || P -> (Q v R) | S -> P | S & ~Q | R
x  0  0  1       1                  1          1         0
valid

2.  P -> (Q v R),  P -> S, ~S |- ~(Q v R)

P Q R S || P -> (Q v R) | P -> S | ~S | ~(Q v R)
0  1  1  0      1                   1       1     0
invalid  (other bad lines are possible as well)

3.  (P -> Q) v (R -> S), P v R  |- Q v S

P Q R S || (P -> Q) v (R -> S) | P v R | Q v S
1  0  0  0                1                  1         0
invalid  (another bad line is possible as well)

4.  (P & Q) -> (R v S), P, ~R |- ~Q v S

P Q R S || (P & Q) -> (R v S) | P | ~R | ~Q v S
1  1  0  x                1              1   1           0
valid