| 1 | Premise: | P-->Q |
| | Conclusion: | ~P--> ~Q |
| | P | Q | P-->Q | ~P-->~Q |
| | T | T | TT F | FTT FT |
| | T | F | TF F | FTT TF |
| | F | T | FT T | TFF FT |
| | F | F | FT F | FTF TF |
| 2 | Premise: | P-->Q |
| | Conclusion: | ~Q-->~P |
| | P | Q | P-->Q | ~Q-->~P |
| | T | T | TT T | FTT FT |
| | T | F | TF F | TFF FT |
| | F | T | FT T | FTT TF |
| | F | F | FT F | TFT TF |
| 3 | Premise: | (P&Q)-->R |
| | | Q-->R |
| | Conclusion: | P-->R |
| | P | Q | R | P&Q | (P&Q)-->R | Q-->R | P-->R |
| | T | T | T | TTT | TTTTT | TTT | TTT |
| | T | T | F | TTT | TTTFF | TFF | TFF |
| | T | F | T | TFF | TFFTT | FTT | TTT |
| | T | F | F | TFF | TFFTF | FTF | TFF |
| | F | T | T | FFT | FFTTT | TTT | FTT |
| | F | T | F | FFT | FFTTF | TFF | FTF |
| | F | F | T | FFF | FFFTT | FTT | FTT |
| | F | F | F | FFF | FFFTF | FTF | FTF |
| 4 | Translate the following argument and use truth tables to test for validity. |
| | If 9 is less than 10 and every odd number less than 10 is divisible by 3, then 9 is divisible by . Therefore if 9 is less than 10 it is divisible by 3. |
| | N=" 9 is less than 10." |
| | O="Every odd number less than 10 is divisible by 3." |
| | D="9 is divisible by 3." |
| | Premise: | (N&O)-->D |
| | | O-->D |
| | Conclusion: | N-->D |
| | N | O | D | (N&O)-->D | O-->D | N-->D |
| | T | T | T | TTTTT | TTT | TTT |
| | T | F | T | TFFTT | FTT | TTT |
| | F | T | T | FFTTT | TTT | FTT |
| | F | F | T | FFFTT | FTT | FTT |
| | T | T | F | TTTFFF | TFF | TFF |
| | T | F | F | TFFTF | FTF | TFF |
| | F | T | F | FFFTTF | TFF | FTF |
| | F | F | F | FFFTF | FTF | FTF |
| 5 | Translate the following argument and use the truth tables to test for validity. |
| | "If it rains tomorrow, I will have a tough commute. If it snows tomorrow, I will have a tough commute. It will either rain or snow tomorrow therefore I will have a tough commute." |
| | R="It rains tomorrow" |
| | S="It snows tomorrow" |
| | T="I will have a tough commute" |
| | Premise: | (~R&~S)-->T |
| | | ~R-->T |
| | | ~S-->T |
| | Conclusion: | (~R&~S)-->T | Answer: | I will have a tough commute tomorrow |
| | R | S | T | (~R&~S)-->T | ~R-->T | ~S-->T |
| | T | T | T | FTFFTTT | FTTT | FTTT |
| | T | T | F | FTFFTTF | FTTF | FTTF |
| | T | F | T | FTFTFTT | FTTT | TFTT |
| | T | F | F | FTFTFTF | FTTF | TFFF |
| | F | T | T | TFFFTTT | TFTT | FTTT |
| | F | T | F | TFFFTTF | TFFF | FTTF |
| | F | F | T | TFTTFTT | TFTT | TFTT |
| | F | F | F | TFTTFFF | TFFF | TFFF |
| Resources: |
| Rieppel, M. (n.d.). Truth Table Generator. Retrieved April 14, 2018, from http://mrieppel.net/prog/truthtable.html |