P Q || P Q C | P | Q.................P Q || P Q C | Q | P
1..0....1..0..1....1...0.................0..1....0..1..1...1...0
.................X
The key to working smoothly with this reverse method is taking full advantage of the forced choices coming from your application of the truth-table rules. It is easy enough to guess at a pattern that will not fit, but that is not enough. We need to know that no pattern will fit. Study the examples below.
for PQARC, RN |- PN
P Q R || P Q A R C | RN | PN
1.....0....1...........0..1..0 1...1 0
In order to keep the conditional true we are forced to have Q be false, which does fit. We know, then, that the pattern is invalid.
P Q R || P Q A R C | RN | PN
1..0..0...1..0..0..0..1...0 1...1 0
for PQORC, RN |- PN
P Q R || P Q O R C | RN | PN
1.....0....1...........0..1..0 1...1 0
Here it no longer matters whether we say Q is true or false. With P true the antecedent in the conditional is automatically true, but this will not fit. We know, then, that the pattern is valid.
P Q R || P Q O R C | RN | PN
1.....0....1.....X...0..1...0 1...1 0
Next: learn about a parallel technique for testing arguments in predicate logic