12. Questions on Truth Tables for Arguments

Truth Tables for Arguments and Testing for Validity:

For each argument below, construct a truth table.  Then, using the table, determine whether the argument is valid or invalid.

Questions:

1. P v (Q & ~R), ~P & (~R -> Q), P -> Q |- ~Q & P
2. P & ~Q , ~P -> (Q & P) |- ~(~P & Q)
3. (P -> ~(Q & R)) -> ~( P v Q), ~(P & (Q & R)) |- P & ~R
4. P & (Q -> ~R) , ~Q & (P v R) , ~P -> ~(Q v P) |- ~P & (~R & Q)