1. 6.4 Truth Tables for Arguments
Propositional Logic
6.4 Truth Tables for Arguments

2. Truth Tables for Arguments
Symbolize the argument using letters for simple propositions.
On one line, write the premises separated by single slashes, then the conclusion separated from the premises by a double slash.
Apply TTFF and TFTF to each letter,* then draw a truth table for each premise individually, and the conclusion individually.
Look for a line where each premise is true but the conclusion is false. If there is such a line, the argument is invalid. If not, it is valid (it isn’t possible for the conclusion to be false when the premises are true).
*Recall this applies only when there are 2 simple statements

3. Truth Tables for Arguments
Step 1: If Greg is right, then you are nuts. Oh, and Greg isn’t right. So, you aren’t nuts. R  N ~R ~N

4. Truth Tables for Arguments
Step 2: If Greg is right, then you are nuts. Oh, and Greg isn’t right. So, you aren’t nuts. R  N / ~R // ~N

5. Truth Tables for Arguments
Step 3: If Greg is right, … R  N / ~R // ~N
Step 4:
Argument is invalid T T T F T F T
It is possible for the premises to be true and the conclusion false T F F F T T F
Recall: an argument is valid if true premises guarantee the conclusion F T T T F F T F T F T F T F