Proving Validity of a Symbolic Argument Using Truth Tables
I am looking to determine the validity of this argument using the truth table method:
P ∨ Q, P → R, ¬R ⊨ Q
I cannot yet embed the image of my truth table on here because I haven't earned emough points of my profile yet, so I will try to explain it the best I can.
I have used the column headers | P | Q | R |¬R | P ∨ Q | P → R | Q |
After filling out this truth table I have found that in row 3, the premises 'P ∨ Q' and 'P → R' are true and yet the conclusion is false, which would indicate that the argument is invalid.
However I am wondering whether I should also take into account the truth value of the premise '¬R'. If I do this, then I find only one critical row (row 6), and here I find the conclusion to be true. As there are no rows where the premises are true and the conclusion is false, I read from this that the argument is valid.
However, I am apprehensive to draw this conclusion; for one because I am not sure whether I have used the correct column headers, and for another because I am not sure whether I should be be looking at '¬R' as a separate premise and considering it's truth value to determine the validity of the conclusion.
As you can probably tell, I am a beginner in logic, so I would appreciate any help to clarify this. Thank you.