| | M5.A1 Truth Table Exercises |
| | Back-up QUESTION SET |
| | 1 | Premise: | P → Q |
| | | Conclusion: | ~P → ~Q |
| | | Solution |
| | | | | | | Premise | | | | conclusion |
| | | P | Q | ~P | ~Q | P→Q | | | | ~P → ~Q |
| | | T | T | F | F | T | | | | T |
| | | T | F | F | T | F | | | | T |
| | | F | T | T | F | T | | | | F |
| | | F | F | T | T | T | | | | T |
| | | Answer: | Notice that in the third row, the conclusion is FALSE while the premise is TRUE. |
| | | | This tells us that the argument is INVALID. |
| | 2 | Premise: | P → Q |
| | | Conclusion: | ~Q → ~P |
| | | Solution |
| | | | | | | Premise | | | | conclusion |
| | | P | Q | ~Q | ~P | P→Q | | | | ~Q → ~P |
| | | T | T | F | F | T | | | | T |
| | | T | F | T | F | F | | | | F |
| | | F | T | F | T | T | | | | T |
| | | F | F | T | T | T | | | | T |
| | Answer: | Notice that in this truth table, there is NO ROW in which conclusion is FALSE while the premise is TRUE. |
| | | This tells us that the argument is VALID. |
| | 3 | Premise: | (P & Q) → R |
| | | | Q → R |
| | | Conclusion: | P → R |
| | | Solution |
| | | | | | Premises | Premise: | | | | Conclusion |
| | P | Q | R | (P & Q) | (P & Q) → R | Q → R | | | | P → R |
| | T | T | T | T | T | T | | | | T |
| | T | T | F | T | F | F | | | | F |
| | T | F | T | F | T | T | | | | T |
| | T | F | F | F | T | T | | | | F |
| | F | T | T | F | T | T | | | | T |
| | F | T | F | F | T | F | | | | T |
| | F | F | T | F | T | T | | | | T |
| | F | F | F | F | T | T | | | | T |
| | Answer: | Notice that in the forth row, the conclusion is FALSE while both premise are TRUE. |
| | | This tells us that the argument is INVALID. |
| | 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 3. |
| | | 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 |
| | | Conclusion: | N →D |
| | | | | | Premises |
| | N | O | D | (N &O) | (N &O)→D | N →D |
| | T | T | T | T | T | T |
| | T | T | F | T | F | F |
| | T | F | T | F | T | T |
| | T | F | F | F | T | F |
| | F | T | T | F | T | T |
| | F | T | F | F | T | T |
| | F | F | T | F | T | T |
| | F | F | F | F | T | T |
| | Answer: | Since the conclusion in the forth row is FALSE while both premise are TRUE, the argument is INVALID. |
| | 5. Translate the following argument and use 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→T |
| | | | S→T |
| | | | R v S |
| | | Conclusion | T | | VALID |
| | | | | Premise | premise | premise | | | | conclusion |
| | R | S | T | R→T | S→T | R v S | | | | T |
| | T | T | T | T | T | T | | | | T |
| | T | T | F | F | F | T | | | | F |
| | T | F | T | T | T | T | | | | T |
| | T | F | F | F | T | T | | | | F |
| | F | T | T | T | T | T | | | | T |
| | F | T | F | T | F | T | | | | F |
| | F | F | T | T | T | F | | | | T |
| | F | F | F | T | T | F | | | | F |
| | Answer: | Since there is NO ROW in this truth table in which conclusion is FALSE while all the three premise is TRUE, the argument is VALID. |
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StaciaM5A2PeerDiscussion.xlsx
