Truth Table: in a table format?

W R ~W W R ~R W R ~W ~(W R ~W) T T F T F F T T F F F T F T F T T T F T F F F T T T T F The argument is:

Premises:

If I increase my withholdings, I will receive a refund on my taxes. (W R) I didn't increase my withholdings. (~W) Conclusion:

Therefore, I didn't get a refund. (~R) To evaluate the conclusion, we need to look at the row(s) where the premises are true. In this case, there is only one row where both premises are true, which is the second row. In this row, the conclusion is false, since it says "I didn't get a refund" (~R), but the truth values for W and R are such that it is possible to get a refund without increasing withholdings. Therefore, we highlight the second row in green, indicating that it is a false conclusion.

Next, we need to evaluate the premises for the row(s) where the conclusion is false. In this case, there is only one row to evaluate, which is the second row. The first premise (W R) is false in this row, since W is true (I didn't increase my withholdings) and R is false (I didn't get a refund). This means that we can ignore the second premise, since the argument is invalid as soon as one premise is false.

Finally, we need to evaluate the validity of the argument by looking for a row where all premises are true and the conclusion is false. In this case, there is no such row, since the argument is invalid in the second row (as shown above). Therefore, the argument is invalid, which means that the conclusion does not follow from the premises.