Use both reverse-method truth tables and consistency trees to test the following argument forms for validity.

1.    P v (Q & R), ~Q  |- P v R

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

P v (Q & R)
~Q
~(P v R)
~P
~R
/       \
   P       Q & R
x           x
valid


2.    P & (Q v R), ~R  |- P & Q

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

P & (Q v R)
~R
~(P & Q)
/        \
~P    ~Q
P      P
Q v R       Q v R
    x           /        \
                  Q          R
                  x              x
valid

                                                                                                         

3.    P -> (Q & R), ~(P v Q) |- R

P Q R ||  P -> (Q & R)  | ~(P v Q)  | R
0  0  0        1                 1              0
invalid

P -> (Q & R)
~(P v Q)
~R
~P
~Q
/         \
~P      Q & R
         x
invalid  (one open branch is enough to show this)



4.    ~P -> (Q v R), ~(P & Q) |- ~R

P Q R ||  ~P -> (Q v R) | ~(P & Q) | ~R
1  0  1           1              1              0
invalid

~P -> (Q v R)
~(P & Q)
~~R
/         \
~P    ~Q
/   \          
P    Q v R        
x      /  \       
    Q  R
       
invalid (again, it was not necessary to complete the tree
since being unable to close the lefthand branch is enough to show
consistency)
Which technique do you find it easier to work with?  For propositional logic either seems quite adequate.  However, when we come back to working with quantifiers we will be able to see how the tree technique may be easier.